What is the Least Common Multiple of 1542 and 1560?

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 1542 and 1560 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1542 and 1560, than apply into the LCM equation.

GCF(1542,1560) = 6
LCM(1542,1560) = ( 1542 × 1560) / 6
LCM(1542,1560) = 2405520 / 6
LCM(1542,1560) = 400920

Least Common Multiple (LCM) of 1542 and 1560 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1542 and 1560. First we will calculate the prime factors of 1542 and 1560.

Prime Factorization of 1542

Prime Factorization of 1560

Now multiplying the highest exponent prime factors to calculate the LCM of 1542 and 1560.

LCM(1542,1560) = 2³ × 3¹ × 257¹ × 5¹ × 13¹
LCM(1542,1560) = 400920