Least Common Multiple of 42 and 45
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 45 the smallest integer that is 630 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 45 is 630.
LCM(42,45) = 630
LCM of 42 and 45
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 45 by Prime method
- Least Common Multiple of 42 and 45 with GCF Formula
LCM of 42 and 45 is 630
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 45. First we will calculate the prime factors of 42 and 45.
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 45
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:
45 = 32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 45.
LCM(42,45) = 21×32×51×71
LCM(42,45) = 630
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 45
List of positive integer factors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
Least Common Multiple of 42 and 45 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 45, than apply into the LCM equation.
GCF(42,45) = 3
LCM(42,45) = ( 42 × 45) / 3
LCM(42,45) = 1890 / 3
LCM(42,45) = 630
Properties of LCM 42 and 45
(i) The LCM of 45 and 42 is associative
LCM of 42 and 45 = LCM of 45 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 45
Frequently Asked Questions on LCM of 42 and 45
1. What is the LCM of 42 and 45?
Answer: LCM of 42 and 45 is 630.
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 45?
Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.
4. How to Find the LCM of 42 and 45?
Answer:
Least Common Multiple of 42 and 45 = 630
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 45
45 = 3 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 = 630 = 2 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 42 and 45 is 630.