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What is the Least Common Multiple of 30048 and 30054?

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 (LCM) of 30048 and 30054 is 150510432.

LCM(30048,30054) = 150510432

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Least Common Multiple of 30048 and 30054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30048 and 30054, than apply into the LCM equation.

GCF(30048,30054) = 6
LCM(30048,30054) = ( 30048 × 30054) / 6
LCM(30048,30054) = 903062592 / 6
LCM(30048,30054) = 150510432

Least Common Multiple (LCM) of 30048 and 30054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30048 and 30054. First we will calculate the prime factors of 30048 and 30054.

Prime Factorization of 30048

Prime factors of 30048 are 2, 3, 313. Prime factorization of 30048 in exponential form is:

30048 = 25 × 31 × 3131

Prime Factorization of 30054

Prime factors of 30054 are 2, 3, 5009. Prime factorization of 30054 in exponential form is:

30054 = 21 × 31 × 50091

Now multiplying the highest exponent prime factors to calculate the LCM of 30048 and 30054.

LCM(30048,30054) = 25 × 31 × 3131 × 50091
LCM(30048,30054) = 150510432