What is the Least Common Multiple of 288 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 288 and 300 is 7200.
LCM(288,300) = 7200
Least Common Multiple of 288 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 288 and 300, than apply into the LCM equation.
GCF(288,300) = 12
LCM(288,300) = ( 288 × 300) / 12
LCM(288,300) = 86400 / 12
LCM(288,300) = 7200
Least Common Multiple (LCM) of 288 and 300 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 288 and 300. First we will calculate the prime factors of 288 and 300.
Prime Factorization of 288
Prime factors of 288 are 2, 3. Prime factorization of 288 in exponential form is:
288 = 25 × 32
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 288 and 300.
LCM(288,300) = 25 × 32 × 52
LCM(288,300) = 7200
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