Least Common Multiple of 39 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 39 and 42 the smallest integer that is 546 that is divisible by both numbers.
Least Common Multiple (LCM) of 39 and 42 is 546.
LCM(39,42) = 546
LCM of 39 and 42
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 39 and 42 by Prime method
- Least Common Multiple of 39 and 42 with GCF Formula
LCM of 39 and 42 is 546
Least common multiple can be found by multiplying the highest exponent prime factors of 39 and 42. First we will calculate the prime factors of 39 and 42.
Prime Factorization of 39
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:
39 = 31×131
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 39 and 42.
LCM(39,42) = 21×31×71×131
LCM(39,42) = 546
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1, 3, 13, 39
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 39 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 39 and 42, than apply into the LCM equation.
GCF(39,42) = 3
LCM(39,42) = ( 39 × 42) / 3
LCM(39,42) = 1638 / 3
LCM(39,42) = 546
Properties of LCM 39 and 42
(i) The LCM of 42 and 39 is associative
LCM of 39 and 42 = LCM of 42 and 39
Related Least Common Multiples of 39
Related Least Common Multiples of 42
Frequently Asked Questions on LCM of 39 and 42
1. What is the LCM of 39 and 42?
Answer: LCM of 39 and 42 is 546.
2. What are the Factors of 39?
Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.
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 39 and 42?
Answer:
Least Common Multiple of 39 and 42 = 546
Step 1: Find the prime factorization of 39
39 = 3 x 13
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 = 546 = 2 x 3 x 7 x 13
Step 4: Therefore, the least common multiple of 39 and 42 is 546.