Least Common Multiple of 42 and 51
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 42 and 51 the smallest integer that is 714 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 51 is 714.
LCM(42,51) = 714
LCM of 42 and 51
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 51 by Prime method
- Least Common Multiple of 42 and 51 with GCF Formula
LCM of 42 and 51 is 714
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 51. First we will calculate the prime factors of 42 and 51.
Prime Factorization of 42
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:
42 = 21×31×71
Prime Factorization of 51
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:
51 = 31×171
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 51.
LCM(42,51) = 21×31×71×171
LCM(42,51) = 714
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1, 3, 17, 51
Least Common Multiple of 42 and 51 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 51, than apply into the LCM equation.
GCF(42,51) = 3
LCM(42,51) = ( 42 × 51) / 3
LCM(42,51) = 2142 / 3
LCM(42,51) = 714
Properties of LCM 42 and 51
(i) The LCM of 51 and 42 is associative
LCM of 42 and 51 = LCM of 51 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 51
Frequently Asked Questions on LCM of 42 and 51
1. What is the LCM of 42 and 51?
Answer: LCM of 42 and 51 is 714.
2. What are the Factors of 42?
Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.
3. What are the Factors of 51?
Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.
4. How to Find the LCM of 42 and 51?
Answer:
Least Common Multiple of 42 and 51 = 714
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 51
51 = 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 = 714 = 2 x 3 x 7 x 17
Step 4: Therefore, the least common multiple of 42 and 51 is 714.
