What is the Least Common Multiple of 7548 and 7564?

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 7548 and 7564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7548 and 7564, than apply into the LCM equation.

GCF(7548,7564) = 4
LCM(7548,7564) = ( 7548 × 7564) / 4
LCM(7548,7564) = 57093072 / 4
LCM(7548,7564) = 14273268

Least Common Multiple (LCM) of 7548 and 7564 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7548 and 7564. First we will calculate the prime factors of 7548 and 7564.

Prime Factorization of 7548

Prime Factorization of 7564

Now multiplying the highest exponent prime factors to calculate the LCM of 7548 and 7564.

LCM(7548,7564) = 2² × 3¹ × 17¹ × 37¹ × 31¹ × 61¹
LCM(7548,7564) = 14273268