What is the Least Common Multiple of 5100 and 5120?

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 5100 and 5120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5100 and 5120, than apply into the LCM equation.

GCF(5100,5120) = 20
LCM(5100,5120) = ( 5100 × 5120) / 20
LCM(5100,5120) = 26112000 / 20
LCM(5100,5120) = 1305600

Least Common Multiple (LCM) of 5100 and 5120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5100 and 5120. First we will calculate the prime factors of 5100 and 5120.

Prime Factorization of 5100

Prime Factorization of 5120

Now multiplying the highest exponent prime factors to calculate the LCM of 5100 and 5120.

LCM(5100,5120) = 2¹⁰ × 3¹ × 5² × 17¹
LCM(5100,5120) = 1305600