What is the Least Common Multiple of 45609 and 45624?

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 45609 and 45624 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45609 and 45624, than apply into the LCM equation.

GCF(45609,45624) = 3
LCM(45609,45624) = ( 45609 × 45624) / 3
LCM(45609,45624) = 2080865016 / 3
LCM(45609,45624) = 693621672

Least Common Multiple (LCM) of 45609 and 45624 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45609 and 45624. First we will calculate the prime factors of 45609 and 45624.

Prime Factorization of 45609

Prime Factorization of 45624

Now multiplying the highest exponent prime factors to calculate the LCM of 45609 and 45624.

LCM(45609,45624) = 3¹ × 23¹ × 661¹ × 2³ × 1901¹
LCM(45609,45624) = 693621672