Least Common Multiple of 42 and 59
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 59 the smallest integer that is 2478 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 59 is 2478.
LCM(42,59) = 2478
LCM of 42 and 59
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 59 by Prime method
- Least Common Multiple of 42 and 59 with GCF Formula
LCM of 42 and 59 is 2478
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 59. First we will calculate the prime factors of 42 and 59.
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 59
| 59 | 59 |
| 1 |
Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:
59 = 591
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 59.
LCM(42,59) = 21×31×71×591
LCM(42,59) = 2478
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 59
List of positive integer factors of 59 that divides 59 without a remainder.
1, 59
Least Common Multiple of 42 and 59 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 59, than apply into the LCM equation.
GCF(42,59) = 1
LCM(42,59) = ( 42 × 59) / 1
LCM(42,59) = 2478 / 1
LCM(42,59) = 2478
Properties of LCM 42 and 59
(i) The LCM of 59 and 42 is associative
LCM of 42 and 59 = LCM of 59 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 59
Frequently Asked Questions on LCM of 42 and 59
1. What is the LCM of 42 and 59?
Answer: LCM of 42 and 59 is 2478.
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 59?
Answer: Factors of 59 are 1, 59. There are 2 integers that are factors of 59. The greatest factor of 59 is 59.
4. How to Find the LCM of 42 and 59?
Answer:
Least Common Multiple of 42 and 59 = 2478
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 59
59 = 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2478 = 2 x 3 x 7 x 59
Step 4: Therefore, the least common multiple of 42 and 59 is 2478.
