Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 107 and 109 the smallest integer that is 11663 that is divisible by both numbers.
Least Common Multiple (LCM) of 107 and 109 is 11663.
LCM(107,109) = 11663
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 107 and 109. First we will calculate the prime factors of 107 and 109.
Prime Factorization of 107
107 | 107 |
1 |
Prime factors of 107 are 107. Prime factorization of 107 in exponential form is:
107 = 1071
Prime Factorization of 109
109 | 109 |
1 |
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 107 and 109.
LCM(107,109) = 1071×1091
LCM(107,109) = 11663
Factors of 107
List of positive integer factors of 107 that divides 107 without a remainder.
1, 107
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 107 and 109, than apply into the LCM equation.
GCF(107,109) = 1
LCM(107,109) = ( 107 × 109) / 1
LCM(107,109) = 11663 / 1
LCM(107,109) = 11663
(i) The LCM of 109 and 107 is associative
LCM of 107 and 109 = LCM of 109 and 107
1. What is the LCM of 107 and 109?
Answer: LCM of 107 and 109 is 11663.
2. What are the Factors of 107?
Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.
3. What are the Factors of 109?
Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.
4. How to Find the LCM of 107 and 109?
Answer:
Least Common Multiple of 107 and 109 = 11663
Step 1: Find the prime factorization of 107
107 = 107
Step 2: Find the prime factorization of 109
109 = 109
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11663 = 107 x 109
Step 4: Therefore, the least common multiple of 107 and 109 is 11663.