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 101 the smallest integer that is 9696 that is divisible by both numbers.
Least Common Multiple (LCM) of 96 and 101 is 9696.
LCM(96,101) = 9696
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 101. First we will calculate the prime factors of 96 and 101.
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 101
101 | 101 |
1 |
Prime factors of 101 are 101. Prime factorization of 101 in exponential form is:
101 = 1011
Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 101.
LCM(96,101) = 25×31×1011
LCM(96,101) = 9696
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 101
List of positive integer factors of 101 that divides 101 without a remainder.
1, 101
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96 and 101, than apply into the LCM equation.
GCF(96,101) = 1
LCM(96,101) = ( 96 × 101) / 1
LCM(96,101) = 9696 / 1
LCM(96,101) = 9696
(i) The LCM of 101 and 96 is associative
LCM of 96 and 101 = LCM of 101 and 96
1. What is the LCM of 96 and 101?
Answer: LCM of 96 and 101 is 9696.
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 101?
Answer: Factors of 101 are 1, 101. There are 2 integers that are factors of 101. The greatest factor of 101 is 101.
4. How to Find the LCM of 96 and 101?
Answer:
Least Common Multiple of 96 and 101 = 9696
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 101
101 = 101
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9696 = 2 x 2 x 2 x 2 x 2 x 3 x 101
Step 4: Therefore, the least common multiple of 96 and 101 is 9696.