Least Common Multiple of 27 and 42
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 27 and 42 the smallest integer that is 378 that is divisible by both numbers.
Least Common Multiple (LCM) of 27 and 42 is 378.
LCM(27,42) = 378
LCM of 27 and 42
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 27 and 42 by Prime method
- Least Common Multiple of 27 and 42 with GCF Formula
LCM of 27 and 42 is 378
Least common multiple can be found by multiplying the highest exponent prime factors of 27 and 42. First we will calculate the prime factors of 27 and 42.
Prime Factorization of 27
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
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
Now multiplying the highest exponent prime factors to calculate the LCM of 27 and 42.
LCM(27,42) = 21×33×71
LCM(27,42) = 378
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1, 3, 9, 27
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42
Least Common Multiple of 27 and 42 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27 and 42, than apply into the LCM equation.
GCF(27,42) = 3
LCM(27,42) = ( 27 × 42) / 3
LCM(27,42) = 1134 / 3
LCM(27,42) = 378
Properties of LCM 27 and 42
(i) The LCM of 42 and 27 is associative
LCM of 27 and 42 = LCM of 42 and 27
Related Least Common Multiples of 27
Related Least Common Multiples of 42
Frequently Asked Questions on LCM of 27 and 42
1. What is the LCM of 27 and 42?
Answer: LCM of 27 and 42 is 378.
2. What are the Factors of 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
3. 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.
4. How to Find the LCM of 27 and 42?
Answer:
Least Common Multiple of 27 and 42 = 378
Step 1: Find the prime factorization of 27
27 = 3 x 3 x 3
Step 2: Find the prime factorization of 42
42 = 2 x 3 x 7
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 27 and 42 is 378.
