What is the Least Common Multiple of 100 and 108?
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 100 and 108 is 2700.
LCM(100,108) = 2700
Least Common Multiple of 100 and 108 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 100 and 108, than apply into the LCM equation.
GCF(100,108) = 4
LCM(100,108) = ( 100 × 108) / 4
LCM(100,108) = 10800 / 4
LCM(100,108) = 2700
Least Common Multiple (LCM) of 100 and 108 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 100 and 108. First we will calculate the prime factors of 100 and 108.
Prime Factorization of 100
Prime factors of 100 are 2, 5. Prime factorization of 100 in exponential form is:
100 = 22 × 52
Prime Factorization of 108
Prime factors of 108 are 2, 3. Prime factorization of 108 in exponential form is:
108 = 22 × 33
Now multiplying the highest exponent prime factors to calculate the LCM of 100 and 108.
LCM(100,108) = 22 × 52 × 33
LCM(100,108) = 2700
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Related Least Common Multiples of 108
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