What is the Least Common Multiple of 15204 and 15219?
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 15204 and 15219 is 77129892.
LCM(15204,15219) = 77129892
Least Common Multiple of 15204 and 15219 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15204 and 15219, than apply into the LCM equation.
GCF(15204,15219) = 3
LCM(15204,15219) = ( 15204 × 15219) / 3
LCM(15204,15219) = 231389676 / 3
LCM(15204,15219) = 77129892
Least Common Multiple (LCM) of 15204 and 15219 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 15204 and 15219. First we will calculate the prime factors of 15204 and 15219.
Prime Factorization of 15204
Prime factors of 15204 are 2, 3, 7, 181. Prime factorization of 15204 in exponential form is:
15204 = 22 × 31 × 71 × 1811
Prime Factorization of 15219
Prime factors of 15219 are 3, 19, 89. Prime factorization of 15219 in exponential form is:
15219 = 32 × 191 × 891
Now multiplying the highest exponent prime factors to calculate the LCM of 15204 and 15219.
LCM(15204,15219) = 22 × 32 × 71 × 1811 × 191 × 891
LCM(15204,15219) = 77129892
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