What is the Least Common Multiple of 30400 and 30407?

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 30400 and 30407 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30400 and 30407, than apply into the LCM equation.

GCF(30400,30407) = 1
LCM(30400,30407) = ( 30400 × 30407) / 1
LCM(30400,30407) = 924372800 / 1
LCM(30400,30407) = 924372800

Least Common Multiple (LCM) of 30400 and 30407 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30400 and 30407. First we will calculate the prime factors of 30400 and 30407.

Prime Factorization of 30400

Prime Factorization of 30407

Now multiplying the highest exponent prime factors to calculate the LCM of 30400 and 30407.

LCM(30400,30407) = 2⁶ × 5² × 19¹ × 13¹ × 2339¹
LCM(30400,30407) = 924372800