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What is the Least Common Multiple of 30814 and 30820?

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 30814 and 30820 is 474843740.

LCM(30814,30820) = 474843740

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Least Common Multiple of 30814 and 30820 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30814 and 30820, than apply into the LCM equation.

GCF(30814,30820) = 2
LCM(30814,30820) = ( 30814 × 30820) / 2
LCM(30814,30820) = 949687480 / 2
LCM(30814,30820) = 474843740

Least Common Multiple (LCM) of 30814 and 30820 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30814 and 30820. First we will calculate the prime factors of 30814 and 30820.

Prime Factorization of 30814

Prime factors of 30814 are 2, 7, 31, 71. Prime factorization of 30814 in exponential form is:

30814 = 21 × 71 × 311 × 711

Prime Factorization of 30820

Prime factors of 30820 are 2, 5, 23, 67. Prime factorization of 30820 in exponential form is:

30820 = 22 × 51 × 231 × 671

Now multiplying the highest exponent prime factors to calculate the LCM of 30814 and 30820.

LCM(30814,30820) = 22 × 71 × 311 × 711 × 51 × 231 × 671
LCM(30814,30820) = 474843740