What is the Least Common Multiple of 75205 and 75225?
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 75205 and 75225 is 1131459225.
LCM(75205,75225) = 1131459225
Least Common Multiple of 75205 and 75225 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75205 and 75225, than apply into the LCM equation.
GCF(75205,75225) = 5
LCM(75205,75225) = ( 75205 × 75225) / 5
LCM(75205,75225) = 5657296125 / 5
LCM(75205,75225) = 1131459225
Least Common Multiple (LCM) of 75205 and 75225 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 75205 and 75225. First we will calculate the prime factors of 75205 and 75225.
Prime Factorization of 75205
Prime factors of 75205 are 5, 13, 89. Prime factorization of 75205 in exponential form is:
75205 = 51 × 132 × 891
Prime Factorization of 75225
Prime factors of 75225 are 3, 5, 17, 59. Prime factorization of 75225 in exponential form is:
75225 = 31 × 52 × 171 × 591
Now multiplying the highest exponent prime factors to calculate the LCM of 75205 and 75225.
LCM(75205,75225) = 52 × 132 × 891 × 31 × 171 × 591
LCM(75205,75225) = 1131459225
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