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What is the Least Common Multiple of 30520 and 30534?

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 30520 and 30534 is 66564120.

LCM(30520,30534) = 66564120

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Least Common Multiple of 30520 and 30534 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30520 and 30534, than apply into the LCM equation.

GCF(30520,30534) = 14
LCM(30520,30534) = ( 30520 × 30534) / 14
LCM(30520,30534) = 931897680 / 14
LCM(30520,30534) = 66564120

Least Common Multiple (LCM) of 30520 and 30534 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30520 and 30534. First we will calculate the prime factors of 30520 and 30534.

Prime Factorization of 30520

Prime factors of 30520 are 2, 5, 7, 109. Prime factorization of 30520 in exponential form is:

30520 = 23 × 51 × 71 × 1091

Prime Factorization of 30534

Prime factors of 30534 are 2, 3, 7, 727. Prime factorization of 30534 in exponential form is:

30534 = 21 × 31 × 71 × 7271

Now multiplying the highest exponent prime factors to calculate the LCM of 30520 and 30534.

LCM(30520,30534) = 23 × 51 × 71 × 1091 × 31 × 7271
LCM(30520,30534) = 66564120