What is the Least Common Multiple of 105 and 109?
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 105 and 109 is 11445.
LCM(105,109) = 11445
Least Common Multiple of 105 and 109 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 109, than apply into the LCM equation.
GCF(105,109) = 1
LCM(105,109) = ( 105 × 109) / 1
LCM(105,109) = 11445 / 1
LCM(105,109) = 11445
Least Common Multiple (LCM) of 105 and 109 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 109. First we will calculate the prime factors of 105 and 109.
Prime Factorization of 105
Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:
105 = 31 × 51 × 71
Prime Factorization of 109
Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:
109 = 1091
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 109.
LCM(105,109) = 31 × 51 × 71 × 1091
LCM(105,109) = 11445
Related Least Common Multiples of 105
- LCM of 105 and 109
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- LCM of 105 and 112
- LCM of 105 and 113
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- LCM of 105 and 117
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- LCM of 105 and 119
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Related Least Common Multiples of 109
- LCM of 109 and 113
- LCM of 109 and 114
- LCM of 109 and 115
- LCM of 109 and 116
- LCM of 109 and 117
- LCM of 109 and 118
- LCM of 109 and 119
- LCM of 109 and 120
- LCM of 109 and 121
- LCM of 109 and 122
- LCM of 109 and 123
- LCM of 109 and 124
- LCM of 109 and 125
- LCM of 109 and 126
- LCM of 109 and 127
- LCM of 109 and 128
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