How do I find the 2 numbers when their LCM and HCF are given?

How do I find the 2 numbers when their LCM and HCF are given?

Relationship between H.C.F. and L.C.M.

1. or, L.C.M. = First Number×Second NumberH.C.F.
2. or, L.C.M. = Product of Two Given NumbersH.C.F.
3. or, H.C.F. = Product of Two Given NumbersL.C.M.

How do you find the LCM and GCD?

Solution

1. The prime factorizations of these numbers are: 12 = 2×2×3. 24 = 2×2×2×3. 36 = 2×2×3×3. 68 = 2×2×17.
2. The common multiples are: 2, 2. So, the greatest common divisor (GCD) is 4. GCD = 2×2 = 4.
3. The least common multiple (LCM) is equal to 1224.

How do you find the GCD of a pair of integers?

Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, to compute gcd(48, 180), we find the prime factorizations 48 = 24 · 31 and 180 = 22 · 32 · 51; the GCD is then 2 · 3 · 5 = 22 · 31 · 50 = 12, as shown in the Venn diagram.

How do you find a number if you only have the LCM?

Reduce the number to its prime factors. Hence list all the factors. Find all the combinations of those factors to produce two numbers. If only LCM is given, there may be a couple of two numbers whose LCM will be the given number.

What two numbers have a LCM of 60?

Answer: As the least common multiple of two numbers is 60 , the two numbers are factors of 60 . Among {1,2,3,4,5,6,10,12,15,20,30,60} , 3 & 10 and 5 & 12 are the only two pair of numbers whose difference is 7 . But Least common multiple of 3 and 10 is 30 .

What is GCD example?

Ans: GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is nothing but the greatest number which divides both of them. For instance GCD of 28 and 20 is 4 and GCD of 56 and 98 is 14.

Is GCD and LCM are same?

The greatest common divisor of two integers, also known as GCD, is the greatest positive integer that divides the two integers. The least common multiple , also known as the LCM, is the smallest number that is divisible by both integer a and b.

What is the maximum of GCD of 2 numbers?

After the whole traversal, we can simply traverse the count array from last index to index 1. If we found an index with a value greater than 1, then this means that it is a divisor of 2 elements and also the max GCD.

What is the LCM of three numbers?

Calculator Use For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30. The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set.

What is HCF example?

HCF : The largest number that divides two or more numbers is the highest common factor (HCF) for those numbers. For example, consider the numbers 30 (2 x 3 x 5), 36 (2 x 2 x 3 x 3), 42 (2 x 3 x 7), 45 (3 x 3 x 5). 3 is the largest number that divides each of these numbers, and hence, is the HCF for these numbers.

How to find the least common multiple for gcd?

The Least common multiple is found by multiplying all the unique factors that appear in either list, i.e. if the factor is common in both, take once and if factors are not in common, consider all of them. So, the LCM is 2 × 3 × 5 × 5 which is 150. Facts about GCD and LCM

How to find the number of pairs with given GCD?

The number of pairs is equal to 2 n. L C M G C D = 60 = 2 2 ∗ 5 ∗ 3 therefore we have 2 3 (we have 3 prime factors) pairs. Could you please explain to me why this is correct? Exactly one of the two members of the pair must be divisible by 2 3 — that’s a choice of 2 options.

Which is the product of LCM and gcd?

The product of LCM and GCD of two numbers is equal to the product of those two numbers. The greatest number that exactly divides the number a, b and c is GCD (a, b, c)

How is the greatest common divisor ( LCM ) found?

The Greatest Common Divisor is found by multiplying all the factors that are common in both the list. The Least common multiple is found by multiplying all the unique factors that appear in either list, i.e. if the factor is common in both, take once and if factors are not in common, consider all of them. So, the LCM is 2 × 3 × 5 × 5 which is 150.