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What is the Least Common Multiple of 9952 and 9972?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 9952 and 9972 is 24810336.

LCM(9952,9972) = 24810336

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Least Common Multiple of 9952 and 9972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9952 and 9972, than apply into the LCM equation.

GCF(9952,9972) = 4
LCM(9952,9972) = ( 9952 × 9972) / 4
LCM(9952,9972) = 99241344 / 4
LCM(9952,9972) = 24810336

Least Common Multiple (LCM) of 9952 and 9972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9952 and 9972. First we will calculate the prime factors of 9952 and 9972.

Prime Factorization of 9952

Prime factors of 9952 are 2, 311. Prime factorization of 9952 in exponential form is:

9952 = 25 × 3111

Prime Factorization of 9972

Prime factors of 9972 are 2, 3, 277. Prime factorization of 9972 in exponential form is:

9972 = 22 × 32 × 2771

Now multiplying the highest exponent prime factors to calculate the LCM of 9952 and 9972.

LCM(9952,9972) = 25 × 3111 × 32 × 2771
LCM(9952,9972) = 24810336