What is the Least Common Multiple of 5040 and 5052?

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 5040 and 5052 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5040 and 5052, than apply into the LCM equation.

GCF(5040,5052) = 12
LCM(5040,5052) = ( 5040 × 5052) / 12
LCM(5040,5052) = 25462080 / 12
LCM(5040,5052) = 2121840

Least Common Multiple (LCM) of 5040 and 5052 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5040 and 5052. First we will calculate the prime factors of 5040 and 5052.

Prime Factorization of 5040

Prime Factorization of 5052

Now multiplying the highest exponent prime factors to calculate the LCM of 5040 and 5052.

LCM(5040,5052) = 2⁴ × 3² × 5¹ × 7¹ × 421¹
LCM(5040,5052) = 2121840