What is the Least Common Multiple of 7140 and 7152?

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 7140 and 7152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7140 and 7152, than apply into the LCM equation.

GCF(7140,7152) = 12
LCM(7140,7152) = ( 7140 × 7152) / 12
LCM(7140,7152) = 51065280 / 12
LCM(7140,7152) = 4255440

Least Common Multiple (LCM) of 7140 and 7152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7140 and 7152. First we will calculate the prime factors of 7140 and 7152.

Prime Factorization of 7140

Prime Factorization of 7152

Now multiplying the highest exponent prime factors to calculate the LCM of 7140 and 7152.

LCM(7140,7152) = 2⁴ × 3¹ × 5¹ × 7¹ × 17¹ × 149¹
LCM(7140,7152) = 4255440