Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 96 and 106 the smallest integer that is 5088 that is divisible by both numbers.
Least Common Multiple (LCM) of 96 and 106 is 5088.
LCM(96,106) = 5088
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 96 and 106. First we will calculate the prime factors of 96 and 106.
Prime Factorization of 96
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:
96 = 25×31
Prime Factorization of 106
2 | 106 |
53 | 53 |
1 |
Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:
106 = 21×531
Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 106.
LCM(96,106) = 25×31×531
LCM(96,106) = 5088
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1, 2, 53, 106
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96 and 106, than apply into the LCM equation.
GCF(96,106) = 2
LCM(96,106) = ( 96 × 106) / 2
LCM(96,106) = 10176 / 2
LCM(96,106) = 5088
(i) The LCM of 106 and 96 is associative
LCM of 96 and 106 = LCM of 106 and 96
1. What is the LCM of 96 and 106?
Answer: LCM of 96 and 106 is 5088.
2. What are the Factors of 96?
Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.
3. What are the Factors of 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
4. How to Find the LCM of 96 and 106?
Answer:
Least Common Multiple of 96 and 106 = 5088
Step 1: Find the prime factorization of 96
96 = 2 x 2 x 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 106
106 = 2 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5088 = 2 x 2 x 2 x 2 x 2 x 3 x 53
Step 4: Therefore, the least common multiple of 96 and 106 is 5088.