Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 100 and 102 the smallest integer that is 5100 that is divisible by both numbers.
Least Common Multiple (LCM) of 100 and 102 is 5100.
LCM(100,102) = 5100
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 100 and 102. First we will calculate the prime factors of 100 and 102.
Prime Factorization of 100
2 | 100 |
2 | 50 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:
100 = 22×52
Prime Factorization of 102
2 | 102 |
3 | 51 |
17 | 17 |
1 |
Prime factors of 102 are 2, 3,17. Prime factorization of 102 in exponential form is:
102 = 21×31×171
Now multiplying the highest exponent prime factors to calculate the LCM of 100 and 102.
LCM(100,102) = 22×31×52×171
LCM(100,102) = 5100
Factors of 100
List of positive integer factors of 100 that divides 100 without a remainder.
1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 102
List of positive integer factors of 102 that divides 102 without a remainder.
1, 2, 3, 6, 17, 34, 51, 102
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 100 and 102, than apply into the LCM equation.
GCF(100,102) = 2
LCM(100,102) = ( 100 × 102) / 2
LCM(100,102) = 10200 / 2
LCM(100,102) = 5100
(i) The LCM of 102 and 100 is associative
LCM of 100 and 102 = LCM of 102 and 100
1. What is the LCM of 100 and 102?
Answer: LCM of 100 and 102 is 5100.
2. What are the Factors of 100?
Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.
3. What are the Factors of 102?
Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.
4. How to Find the LCM of 100 and 102?
Answer:
Least Common Multiple of 100 and 102 = 5100
Step 1: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 102
102 = 2 x 3 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5100 = 2 x 2 x 3 x 5 x 5 x 17
Step 4: Therefore, the least common multiple of 100 and 102 is 5100.