What is the Least Common Multiple of 67740 and 67749?

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 67740 and 67749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67740 and 67749, than apply into the LCM equation.

GCF(67740,67749) = 3
LCM(67740,67749) = ( 67740 × 67749) / 3
LCM(67740,67749) = 4589317260 / 3
LCM(67740,67749) = 1529772420

Least Common Multiple (LCM) of 67740 and 67749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67740 and 67749. First we will calculate the prime factors of 67740 and 67749.

Prime Factorization of 67740

Prime Factorization of 67749

Now multiplying the highest exponent prime factors to calculate the LCM of 67740 and 67749.

LCM(67740,67749) = 2² × 3¹ × 5¹ × 1129¹ × 11¹ × 2053¹
LCM(67740,67749) = 1529772420