What is the Least Common Multiple of 71904 and 71920?

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 71904 and 71920 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71904 and 71920, than apply into the LCM equation.

GCF(71904,71920) = 16
LCM(71904,71920) = ( 71904 × 71920) / 16
LCM(71904,71920) = 5171335680 / 16
LCM(71904,71920) = 323208480

Least Common Multiple (LCM) of 71904 and 71920 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71904 and 71920. First we will calculate the prime factors of 71904 and 71920.

Prime Factorization of 71904

Prime Factorization of 71920

Now multiplying the highest exponent prime factors to calculate the LCM of 71904 and 71920.

LCM(71904,71920) = 2⁵ × 3¹ × 7¹ × 107¹ × 5¹ × 29¹ × 31¹
LCM(71904,71920) = 323208480