Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2136 and 2139 the smallest integer that is 1522968 that is divisible by both numbers.
Least Common Multiple (LCM) of 2136 and 2139 is 1522968.
LCM(2136,2139) = 1522968
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 2136 and 2139. First we will calculate the prime factors of 2136 and 2139.
Prime Factorization of 2136
2 | 2136 |
2 | 1068 |
2 | 534 |
3 | 267 |
89 | 89 |
1 |
Prime factors of 2136 are 2, 3,89. Prime factorization of 2136 in exponential form is:
2136 = 23×31×891
Prime Factorization of 2139
3 | 2139 |
23 | 713 |
31 | 31 |
1 |
Prime factors of 2139 are 3, 23,31. Prime factorization of 2139 in exponential form is:
2139 = 31×231×311
Now multiplying the highest exponent prime factors to calculate the LCM of 2136 and 2139.
LCM(2136,2139) = 23×31×231×311×891
LCM(2136,2139) = 1522968
Factors of 2136
List of positive integer factors of 2136 that divides 2136 without a remainder.
1, 2, 3, 4, 6, 8, 12, 24, 89, 178, 267, 356, 534, 712, 1068, 2136
Factors of 2139
List of positive integer factors of 2139 that divides 2139 without a remainder.
1, 3, 23, 31, 69, 93, 713, 2139
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2136 and 2139, than apply into the LCM equation.
GCF(2136,2139) = 3
LCM(2136,2139) = ( 2136 × 2139) / 3
LCM(2136,2139) = 4568904 / 3
LCM(2136,2139) = 1522968
(i) The LCM of 2139 and 2136 is associative
LCM of 2136 and 2139 = LCM of 2139 and 2136
1. What is the LCM of 2136 and 2139?
Answer: LCM of 2136 and 2139 is 1522968.
2. What are the Factors of 2136?
Answer: Factors of 2136 are 1, 2, 3, 4, 6, 8, 12, 24, 89, 178, 267, 356, 534, 712, 1068, 2136. There are 16 integers that are factors of 2136. The greatest factor of 2136 is 2136.
3. What are the Factors of 2139?
Answer: Factors of 2139 are 1, 3, 23, 31, 69, 93, 713, 2139. There are 8 integers that are factors of 2139. The greatest factor of 2139 is 2139.
4. How to Find the LCM of 2136 and 2139?
Answer:
Least Common Multiple of 2136 and 2139 = 1522968
Step 1: Find the prime factorization of 2136
2136 = 2 x 2 x 2 x 3 x 89
Step 2: Find the prime factorization of 2139
2139 = 3 x 23 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1522968 = 2 x 2 x 2 x 3 x 23 x 31 x 89
Step 4: Therefore, the least common multiple of 2136 and 2139 is 1522968.