Least Common Multiple of 42 and 50
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 50 the smallest integer that is 1050 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 50 is 1050.
LCM(42,50) = 1050
LCM of 42 and 50
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 50 by Prime method
- Least Common Multiple of 42 and 50 with GCF Formula
LCM of 42 and 50 is 1050
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 50. First we will calculate the prime factors of 42 and 50.
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 50
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 50 are 2,5. Prime factorization of 50 in exponential form is:
50 = 21×52
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 50.
LCM(42,50) = 21×31×52×71
LCM(42,50) = 1050
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 50
List of positive integer factors of 50 that divides 50 without a remainder.
1, 2, 5, 10, 25, 50
Least Common Multiple of 42 and 50 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 50, than apply into the LCM equation.
GCF(42,50) = 2
LCM(42,50) = ( 42 × 50) / 2
LCM(42,50) = 2100 / 2
LCM(42,50) = 1050
Properties of LCM 42 and 50
(i) The LCM of 50 and 42 is associative
LCM of 42 and 50 = LCM of 50 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 50
Frequently Asked Questions on LCM of 42 and 50
1. What is the LCM of 42 and 50?
Answer: LCM of 42 and 50 is 1050.
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 50?
Answer: Factors of 50 are 1, 2, 5, 10, 25, 50. There are 6 integers that are factors of 50. The greatest factor of 50 is 50.
4. How to Find the LCM of 42 and 50?
Answer:
Least Common Multiple of 42 and 50 = 1050
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 50
50 = 2 x 5 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 = 1050 = 2 x 3 x 5 x 5 x 7
Step 4: Therefore, the least common multiple of 42 and 50 is 1050.
