Least Common Multiple of 42 and 54
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 54 the smallest integer that is 378 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 54 is 378.
LCM(42,54) = 378
LCM of 42 and 54
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 54 by Prime method
- Least Common Multiple of 42 and 54 with GCF Formula
LCM of 42 and 54 is 378
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 54. First we will calculate the prime factors of 42 and 54.
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 54
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:
54 = 21×33
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 54.
LCM(42,54) = 21×33×71
LCM(42,54) = 378
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 54
List of positive integer factors of 54 that divides 54 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54
Least Common Multiple of 42 and 54 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 54, than apply into the LCM equation.
GCF(42,54) = 6
LCM(42,54) = ( 42 × 54) / 6
LCM(42,54) = 2268 / 6
LCM(42,54) = 378
Properties of LCM 42 and 54
(i) The LCM of 54 and 42 is associative
LCM of 42 and 54 = LCM of 54 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 54
Frequently Asked Questions on LCM of 42 and 54
1. What is the LCM of 42 and 54?
Answer: LCM of 42 and 54 is 378.
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 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
4. How to Find the LCM of 42 and 54?
Answer:
Least Common Multiple of 42 and 54 = 378
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 378 = 2 x 3 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 42 and 54 is 378.