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 108 the smallest integer that is 11556 that is divisible by both numbers.
Least Common Multiple (LCM) of 107 and 108 is 11556.
LCM(107,108) = 11556
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 108. First we will calculate the prime factors of 107 and 108.
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 108
2 | 108 |
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
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 107 and 108.
LCM(107,108) = 22×33×1071
LCM(107,108) = 11556
Factors of 107
List of positive integer factors of 107 that divides 107 without a remainder.
1, 107
Factors of 108
List of positive integer factors of 108 that divides 108 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 107 and 108, than apply into the LCM equation.
GCF(107,108) = 1
LCM(107,108) = ( 107 × 108) / 1
LCM(107,108) = 11556 / 1
LCM(107,108) = 11556
(i) The LCM of 108 and 107 is associative
LCM of 107 and 108 = LCM of 108 and 107
1. What is the LCM of 107 and 108?
Answer: LCM of 107 and 108 is 11556.
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 108?
Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.
4. How to Find the LCM of 107 and 108?
Answer:
Least Common Multiple of 107 and 108 = 11556
Step 1: Find the prime factorization of 107
107 = 107
Step 2: Find the prime factorization of 108
108 = 2 x 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11556 = 2 x 2 x 3 x 3 x 3 x 107
Step 4: Therefore, the least common multiple of 107 and 108 is 11556.