Least Common Multiple of 42 and 57
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 57 the smallest integer that is 798 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 57 is 798.
LCM(42,57) = 798
LCM of 42 and 57
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 57 by Prime method
- Least Common Multiple of 42 and 57 with GCF Formula
LCM of 42 and 57 is 798
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 57. First we will calculate the prime factors of 42 and 57.
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 57
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 57 are 3,19. Prime factorization of 57 in exponential form is:
57 = 31×191
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 57.
LCM(42,57) = 21×31×71×191
LCM(42,57) = 798
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 57
List of positive integer factors of 57 that divides 57 without a remainder.
1, 3, 19, 57
Least Common Multiple of 42 and 57 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 57, than apply into the LCM equation.
GCF(42,57) = 3
LCM(42,57) = ( 42 × 57) / 3
LCM(42,57) = 2394 / 3
LCM(42,57) = 798
Properties of LCM 42 and 57
(i) The LCM of 57 and 42 is associative
LCM of 42 and 57 = LCM of 57 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 57
Frequently Asked Questions on LCM of 42 and 57
1. What is the LCM of 42 and 57?
Answer: LCM of 42 and 57 is 798.
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 57?
Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.
4. How to Find the LCM of 42 and 57?
Answer:
Least Common Multiple of 42 and 57 = 798
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 57
57 = 3 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 798 = 2 x 3 x 7 x 19
Step 4: Therefore, the least common multiple of 42 and 57 is 798.
