What is the Least Common Multiple of 71952 and 71964?

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 of 71952 and 71964 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71952 and 71964, than apply into the LCM equation.

GCF(71952,71964) = 12
LCM(71952,71964) = ( 71952 × 71964) / 12
LCM(71952,71964) = 5177953728 / 12
LCM(71952,71964) = 431496144

Least Common Multiple (LCM) of 71952 and 71964 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71952 and 71964. First we will calculate the prime factors of 71952 and 71964.

Prime Factorization of 71952

Prime Factorization of 71964

Now multiplying the highest exponent prime factors to calculate the LCM of 71952 and 71964.

LCM(71952,71964) = 2⁴ × 3² × 1499¹ × 1999¹
LCM(71952,71964) = 431496144