Least Common Multiple of 30 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 30 and 42 the smallest integer that is 210 that is divisible by both numbers.
Least Common Multiple (LCM) of 30 and 42 is 210.
LCM(30,42) = 210
LCM of 30 and 42
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 30 and 42 by Prime method
- Least Common Multiple of 30 and 42 with GCF Formula
LCM of 30 and 42 is 210
Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 42. First we will calculate the prime factors of 30 and 42.
Prime Factorization of 30
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:
30 = 21×31×51
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 30 and 42.
LCM(30,42) = 21×31×51×71
LCM(30,42) = 210
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1, 2, 3, 5, 6, 10, 15, 30
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 30 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 30 and 42, than apply into the LCM equation.
GCF(30,42) = 6
LCM(30,42) = ( 30 × 42) / 6
LCM(30,42) = 1260 / 6
LCM(30,42) = 210
Properties of LCM 30 and 42
(i) The LCM of 42 and 30 is associative
LCM of 30 and 42 = LCM of 42 and 30
Related Least Common Multiples of 30
Related Least Common Multiples of 42
Frequently Asked Questions on LCM of 30 and 42
1. What is the LCM of 30 and 42?
Answer: LCM of 30 and 42 is 210.
2. What are the Factors of 30?
Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.
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 30 and 42?
Answer:
Least Common Multiple of 30 and 42 = 210
Step 1: Find the prime factorization of 30
30 = 2 x 3 x 5
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 = 210 = 2 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 30 and 42 is 210.
