What is the Least Common Multiple of 10320 and 10324?

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 10320 and 10324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10320 and 10324, than apply into the LCM equation.

GCF(10320,10324) = 4
LCM(10320,10324) = ( 10320 × 10324) / 4
LCM(10320,10324) = 106543680 / 4
LCM(10320,10324) = 26635920

Least Common Multiple (LCM) of 10320 and 10324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10320 and 10324. First we will calculate the prime factors of 10320 and 10324.

Prime Factorization of 10320

Prime Factorization of 10324

Now multiplying the highest exponent prime factors to calculate the LCM of 10320 and 10324.

LCM(10320,10324) = 2⁴ × 3¹ × 5¹ × 43¹ × 29¹ × 89¹
LCM(10320,10324) = 26635920