What is the Least Common Multiple of 284 and 300?
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 284 and 300 is 21300.
LCM(284,300) = 21300
Least Common Multiple of 284 and 300 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 284 and 300, than apply into the LCM equation.
GCF(284,300) = 4
LCM(284,300) = ( 284 × 300) / 4
LCM(284,300) = 85200 / 4
LCM(284,300) = 21300
Least Common Multiple (LCM) of 284 and 300 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 284 and 300. First we will calculate the prime factors of 284 and 300.
Prime Factorization of 284
Prime factors of 284 are 2, 71. Prime factorization of 284 in exponential form is:
284 = 22 × 711
Prime Factorization of 300
Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:
300 = 22 × 31 × 52
Now multiplying the highest exponent prime factors to calculate the LCM of 284 and 300.
LCM(284,300) = 22 × 711 × 31 × 52
LCM(284,300) = 21300
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