What is the Least Common Multiple of 54960 and 54978?

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 54960 and 54978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54960 and 54978, than apply into the LCM equation.

GCF(54960,54978) = 6
LCM(54960,54978) = ( 54960 × 54978) / 6
LCM(54960,54978) = 3021590880 / 6
LCM(54960,54978) = 503598480

Least Common Multiple (LCM) of 54960 and 54978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54960 and 54978. First we will calculate the prime factors of 54960 and 54978.

Prime Factorization of 54960

Prime Factorization of 54978

Now multiplying the highest exponent prime factors to calculate the LCM of 54960 and 54978.

LCM(54960,54978) = 2⁴ × 3¹ × 5¹ × 229¹ × 7² × 11¹ × 17¹
LCM(54960,54978) = 503598480