Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2142 and 2145 the smallest integer that is 1531530 that is divisible by both numbers.
Least Common Multiple (LCM) of 2142 and 2145 is 1531530.
LCM(2142,2145) = 1531530
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 2142 and 2145. First we will calculate the prime factors of 2142 and 2145.
Prime Factorization of 2142
2 | 2142 |
3 | 1071 |
3 | 357 |
7 | 119 |
17 | 17 |
1 |
Prime factors of 2142 are 2, 3, 7,17. Prime factorization of 2142 in exponential form is:
2142 = 21×32×71×171
Prime Factorization of 2145
3 | 2145 |
5 | 715 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 2145 are 3, 5, 11,13. Prime factorization of 2145 in exponential form is:
2145 = 31×51×111×131
Now multiplying the highest exponent prime factors to calculate the LCM of 2142 and 2145.
LCM(2142,2145) = 21×32×51×71×111×131×171
LCM(2142,2145) = 1531530
Factors of 2142
List of positive integer factors of 2142 that divides 2142 without a remainder.
1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142
Factors of 2145
List of positive integer factors of 2145 that divides 2145 without a remainder.
1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2142 and 2145, than apply into the LCM equation.
GCF(2142,2145) = 3
LCM(2142,2145) = ( 2142 × 2145) / 3
LCM(2142,2145) = 4594590 / 3
LCM(2142,2145) = 1531530
(i) The LCM of 2145 and 2142 is associative
LCM of 2142 and 2145 = LCM of 2145 and 2142
1. What is the LCM of 2142 and 2145?
Answer: LCM of 2142 and 2145 is 1531530.
2. What are the Factors of 2142?
Answer: Factors of 2142 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142. There are 24 integers that are factors of 2142. The greatest factor of 2142 is 2142.
3. What are the Factors of 2145?
Answer: Factors of 2145 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145. There are 16 integers that are factors of 2145. The greatest factor of 2145 is 2145.
4. How to Find the LCM of 2142 and 2145?
Answer:
Least Common Multiple of 2142 and 2145 = 1531530
Step 1: Find the prime factorization of 2142
2142 = 2 x 3 x 3 x 7 x 17
Step 2: Find the prime factorization of 2145
2145 = 3 x 5 x 11 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1531530 = 2 x 3 x 3 x 5 x 7 x 11 x 13 x 17
Step 4: Therefore, the least common multiple of 2142 and 2145 is 1531530.