Least Common Multiple of 42 and 53
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 53 the smallest integer that is 2226 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 53 is 2226.
LCM(42,53) = 2226
LCM of 42 and 53
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 53 by Prime method
- Least Common Multiple of 42 and 53 with GCF Formula
LCM of 42 and 53 is 2226
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 53. First we will calculate the prime factors of 42 and 53.
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 53
| 53 | 53 |
| 1 |
Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:
53 = 531
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 53.
LCM(42,53) = 21×31×71×531
LCM(42,53) = 2226
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 53
List of positive integer factors of 53 that divides 53 without a remainder.
1, 53
Least Common Multiple of 42 and 53 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 53, than apply into the LCM equation.
GCF(42,53) = 1
LCM(42,53) = ( 42 × 53) / 1
LCM(42,53) = 2226 / 1
LCM(42,53) = 2226
Properties of LCM 42 and 53
(i) The LCM of 53 and 42 is associative
LCM of 42 and 53 = LCM of 53 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 53
Frequently Asked Questions on LCM of 42 and 53
1. What is the LCM of 42 and 53?
Answer: LCM of 42 and 53 is 2226.
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 53?
Answer: Factors of 53 are 1, 53. There are 2 integers that are factors of 53. The greatest factor of 53 is 53.
4. How to Find the LCM of 42 and 53?
Answer:
Least Common Multiple of 42 and 53 = 2226
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 53
53 = 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2226 = 2 x 3 x 7 x 53
Step 4: Therefore, the least common multiple of 42 and 53 is 2226.
