What is the Least Common Multiple of 39738 and 39744?

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 39738 and 39744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39738 and 39744, than apply into the LCM equation.

GCF(39738,39744) = 6
LCM(39738,39744) = ( 39738 × 39744) / 6
LCM(39738,39744) = 1579347072 / 6
LCM(39738,39744) = 263224512

Least Common Multiple (LCM) of 39738 and 39744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39738 and 39744. First we will calculate the prime factors of 39738 and 39744.

Prime Factorization of 39738

Prime Factorization of 39744

Now multiplying the highest exponent prime factors to calculate the LCM of 39738 and 39744.

LCM(39738,39744) = 2⁶ × 3³ × 37¹ × 179¹ × 23¹
LCM(39738,39744) = 263224512