What is the Least Common Multiple of 51504 and 51509?

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 51504 and 51509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51504 and 51509, than apply into the LCM equation.

GCF(51504,51509) = 1
LCM(51504,51509) = ( 51504 × 51509) / 1
LCM(51504,51509) = 2652919536 / 1
LCM(51504,51509) = 2652919536

Least Common Multiple (LCM) of 51504 and 51509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51504 and 51509. First we will calculate the prime factors of 51504 and 51509.

Prime Factorization of 51504

Prime Factorization of 51509

Now multiplying the highest exponent prime factors to calculate the LCM of 51504 and 51509.

LCM(51504,51509) = 2⁴ × 3¹ × 29¹ × 37¹ × 19¹ × 2711¹
LCM(51504,51509) = 2652919536