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What is the Least Common Multiple of 77952 and 77965?

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 77952 and 77965 is 6077527680.

LCM(77952,77965) = 6077527680

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Least Common Multiple of 77952 and 77965 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77952 and 77965, than apply into the LCM equation.

GCF(77952,77965) = 1
LCM(77952,77965) = ( 77952 × 77965) / 1
LCM(77952,77965) = 6077527680 / 1
LCM(77952,77965) = 6077527680

Least Common Multiple (LCM) of 77952 and 77965 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 77952 and 77965. First we will calculate the prime factors of 77952 and 77965.

Prime Factorization of 77952

Prime factors of 77952 are 2, 3, 7, 29. Prime factorization of 77952 in exponential form is:

77952 = 27 × 31 × 71 × 291

Prime Factorization of 77965

Prime factors of 77965 are 5, 31, 503. Prime factorization of 77965 in exponential form is:

77965 = 51 × 311 × 5031

Now multiplying the highest exponent prime factors to calculate the LCM of 77952 and 77965.

LCM(77952,77965) = 27 × 31 × 71 × 291 × 51 × 311 × 5031
LCM(77952,77965) = 6077527680