Least Common Multiple of 42 and 60
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 60 the smallest integer that is 420 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 60 is 420.
LCM(42,60) = 420
LCM of 42 and 60
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 60 by Prime method
- Least Common Multiple of 42 and 60 with GCF Formula
LCM of 42 and 60 is 420
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 60. First we will calculate the prime factors of 42 and 60.
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 60
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:
60 = 22×31×51
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 60.
LCM(42,60) = 22×31×51×71
LCM(42,60) = 420
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 60
List of positive integer factors of 60 that divides 60 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Least Common Multiple of 42 and 60 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 60, than apply into the LCM equation.
GCF(42,60) = 6
LCM(42,60) = ( 42 × 60) / 6
LCM(42,60) = 2520 / 6
LCM(42,60) = 420
Properties of LCM 42 and 60
(i) The LCM of 60 and 42 is associative
LCM of 42 and 60 = LCM of 60 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 60
Frequently Asked Questions on LCM of 42 and 60
1. What is the LCM of 42 and 60?
Answer: LCM of 42 and 60 is 420.
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 60?
Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.
4. How to Find the LCM of 42 and 60?
Answer:
Least Common Multiple of 42 and 60 = 420
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 60
60 = 2 x 2 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 420 = 2 x 2 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 42 and 60 is 420.
