The hcf of two numbers is 15, and their lcm is 300. if one of the number is 60, the other is

HCF and LCM HCF or the Highest Common Factor of two numbers is the largest number that can divide both the numbers. LCM or the Least Common Multiple is the smallest number that is evenly divisible by both the numbers. LCM is also known as Least Common Divisor. Now that we know what LCM and HCF are, how do we find two numbers when only their HCF and LCM are known? Finding two numbers when their HCF and LCM are given: Let us take any two numbers a, b, and let us say their HCF and LCM are s and y respectively. To find out the two numbers a and b, we must first understand the relationship between the two numbers and their HCF and LCM. For any two numbers, the product of the two numbers is equal to the product of their HCF and LCM. Let us take the example of 10 and 15. The HCF is 5 and the LCM is 30. Now, the product of the two numbers is 10✕15 = 150 and this is equal to the product of the HCF and LCM which is 5 ✕ 30 = 150 Now that we have understood the relationship between the numbers and their HCF and LCM, we can find the two numbers by taking out the factors of the products of the HCF and LCM. We then eliminate the numbers which have a different HCF or LCM and any remaining pair is the number we are looking for. Note that there could be more than one pair of numbers that have the same HCF and LCM. Taking the above example, let us find two numbers a and b, and their HCF is 5 while their LCM is 30. Now we know that a ✕ b = 5✕30 = 150 Let us factorize the product 150. Factors ...

Two numbers have a highest common factor of $12$ and a lowest common multiple of $600$. Besides $12$ and $600$ themselves , find another pair of numbers that fulfill the above condition . I'm not sure how to carry on from my working - $$HCF= 2^2 \times 3 = 12\;\;\;\&\;\;\; LCM= 2^3 \times 3 \times 5^2 = 600 $$ so your pair of numbers both have 2*2*3 as a factor. you know that one of them must have 5^2 as a factor - if both had 5 as a factor, the HCF would be 60. let these numbers be denoted a and b - a = 2*2*3 * .., b= 2*2*3 * 5*5 * ... one number must include 2^3 - so we divide both numbers by their common factor of 12, and find that 50 = ab, and b contains 5^2, or 25 - so a(b/25) = 2 , so either a or b contains 2^3. thus, your candidates are a = 2^3 *3 = 24 or 2^2 * 3 = 12 b = 2^2 * 3 * 5^2 = 300 , and b = 2^3*3*5^2 =600 so your pairs are 24,30 or 12,600 There is a general method. Write $$ \begin $$ Exchanging the two powers of $5$ will give the same result. Can you see why this method gives you all the possibilities? Hint Think of the definition of gcd and lcm in terms of factorizations. We want to find natural numbers $a$ and $b$ such that $gcd(a,b)=12$ and $lcm(a,b)=600$. Let $a_p$ be the exponent of $p$ in the factorization of $a$. Analogously for $b$. Then all pairs $a,b$ come from solutions of $\min(a_2,b_2)=2,\qquad \max(a_2,b_2)=3$ $\min(a_3,b_3)=1,\qquad \max(a_3,b_3)=1$ $\min(a_5,b_5)=0,\qquad \max(a_5,b_5)=2$ Therefore $(a_2,b_2) \in \$ a total of $2 \cdot 1 \...

• Course • NCERT • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • IIT JEE • Exam • JEE MAINS • JEE ADVANCED • X BOARDS • XII BOARDS • NEET • Neet Previous Year (Year Wise) • Physics Previous Year • Chemistry Previous Year • Biology Previous Year • Neet All Sample Papers • Sample Papers Biology • Sample Papers Physics • Sample Papers Chemistry • Download PDF's • Class 12 • Class 11 • Class 10 • Class 9 • Class 8 • Class 7 • Class 6 • Exam Corner • Online Class • Quiz • Ask Doubt on Whatsapp • Search Doubtnut • English Dictionary • Toppers Talk • Blog • Download • Get App Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams. Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. G...

Let the two numbers be a & b Now, Product of the two numbers = product of the H.C.F & L.C.M of two numbers Thus, a*b = 4*60 or, a*b = 240............(1) Now, Since the H.C.F of a & b is 4 Thus, these numbers can be represented as :- a = 4m & b = 4n........(2) Using (2) in (1) we get 4a*4b = 240 or, 16m*n = 240 or, m*n = 15...........(3) Now, the possible combinations of m & n can be (1,15) ; (15,1) ; (3,5) & (5,3) Thus, a = 12 & b = 20 or vice versa or, a = 4 & b = 60 or vice versa Denote the numbers by x and y. By the conditions 4 is a factor of x and x is a factor of 60. So x=4m for some natural m and 60=x*n for some natural n. Therefore 60=x*n=4*m*n, so 15=m*n and m is a factor of 15. There are not so many factors of 15: 1, 3, 5 and 15. This means that x=4m, i.e. x can be 4, 12, 20 or 60, and the same we can state about y. Now simply try all variants: x=4, y=4 -- no, LCM is 4, not 60. x=4, y=12 -- no, LCM=12. x=4, y=20 -- no, LCM=20. x=4, y=60 -- yes, HCF=4 and LCM=60. x=12, y=12 -- no, LCM=12. x=12, y=20 -- yes! x=12, y=60 -- no, HCF=12. x=20, y=20 -- no, LCM=20. x=20, y=60 -- no, HCF=20. x=60, y=60 -- no, LCM=60. The answer ( two variants): 4 and 60, 12 and 20. (60, 4 and 20, 12 are the same pairs). See eNotes Ad-Free

What is LCM of Two Numbers? The LCM of two numbers or the least common multiple of two numbers is the smallest number which is exactly divisible by two numbers and it is also a common multiple of those two numbers. For example: Take any two numbers such as 23 and 46, let's find the LCM of these two numbers. Multiples of 23 = 23, 46, 69, 92, 115, 138 and so on. Multiples of 46 = 46, 92, 138, 184 and so on. Now take out the smallest common multiple of 23 and 46. We can see that the smallest common multiple is 46. So the LCM of 23 and 46 is 46. Therefore, 46 is the smallest common multiple or LCM of two numbers which is exactly divisible by both the numbers. How to Find LCM of Two Numbers? LCM of two numbers can be calculatedby using four main methods. These four methods to find LCM are discussed below. • Listing Multiples Method • Prime Factorization Method • Division Method • HCF method Finding LCM of Two Numbers by Listing Multiples Method In the listing multiples method, we have to write down the multiples of two numbers up to the first common multiple. For example, find LCM of 5 and 9. Multiples of number 5 = 5, 10,15, 20, 25, 30, 35, 40, 45 and so on. Multiples of number 9 = 9, 18, 27, 36, 45 and so on. The first smallestcommon multiple is 45, of numbers 5 and 9. Hence the LCM of the two numbers is 45. Finding LCM of Two Numbers by Prime Factorization Method In this method, first, write down all the prime factors of two numbers then multiply each factor with the highest...

The H.C.F is also known as the Highest Common Factor for any two given numbers and has been the other number that is possibly counted as the highest. This individual number that is seen as highest can divide both the numerals while leaving no remainder. The same is also identified as the G.C.D and/or Greatest Common Divisor. The L.C.M., on the other hand, is identified as the Least Common Multiple. The same can be elaborated as the numerical value that is considered the lowest and can be divided by the two given numbers. Not only two numbers, but the L.C.M be also calculated on more than two given integers. • Calculating the H.C.F As explained, the H.C.F of two numbers can be a comparatively higher number that can divide the two given numbers; there are numerous methods to calculate the same. This does not leave any remainder and can be explained while analysing an example. Considering two distinct numbers such as 150 and 230 and the H.C.F of the two can be calculated while utilising the following method. 150 can be presented as 150= 2x5x5x3 and for 230 the related presentation is 230=2x5x23. Thus, it can be seen that the numbers that are common in this scenario are 2 and 5. Thus the H.C.F and G.C.D can be identified by the product of both the distinct numbers and that is 10. The result of the H.C.F can be represented as HCF (150, 230) =10. Thus using the aforementioned explanation, a similar calculation can be done on 60 and 40 for an instance where 60= 2x2x3x5 and 40= 2x...