What is the Least Common Multiple of 30720 and 30729?

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 30720 and 30729 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30720 and 30729, than apply into the LCM equation.

GCF(30720,30729) = 3
LCM(30720,30729) = ( 30720 × 30729) / 3
LCM(30720,30729) = 943994880 / 3
LCM(30720,30729) = 314664960

Least Common Multiple (LCM) of 30720 and 30729 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30720 and 30729. First we will calculate the prime factors of 30720 and 30729.

Prime Factorization of 30720

Prime Factorization of 30729

Now multiplying the highest exponent prime factors to calculate the LCM of 30720 and 30729.

LCM(30720,30729) = 2¹¹ × 3¹ × 5¹ × 10243¹
LCM(30720,30729) = 314664960