Least Common Multiple of 42 and 46
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 46 the smallest integer that is 966 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 46 is 966.
LCM(42,46) = 966
LCM of 42 and 46
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 46 by Prime method
- Least Common Multiple of 42 and 46 with GCF Formula
LCM of 42 and 46 is 966
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 46. First we will calculate the prime factors of 42 and 46.
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 46
| 2 | 46 |
| 23 | 23 |
| 1 |
Prime factors of 46 are 2,23. Prime factorization of 46 in exponential form is:
46 = 21×231
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 46.
LCM(42,46) = 21×31×71×231
LCM(42,46) = 966
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 46
List of positive integer factors of 46 that divides 46 without a remainder.
1, 2, 23, 46
Least Common Multiple of 42 and 46 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 46, than apply into the LCM equation.
GCF(42,46) = 2
LCM(42,46) = ( 42 × 46) / 2
LCM(42,46) = 1932 / 2
LCM(42,46) = 966
Properties of LCM 42 and 46
(i) The LCM of 46 and 42 is associative
LCM of 42 and 46 = LCM of 46 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 46
Frequently Asked Questions on LCM of 42 and 46
1. What is the LCM of 42 and 46?
Answer: LCM of 42 and 46 is 966.
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 46?
Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.
4. How to Find the LCM of 42 and 46?
Answer:
Least Common Multiple of 42 and 46 = 966
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 46
46 = 2 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 966 = 2 x 3 x 7 x 23
Step 4: Therefore, the least common multiple of 42 and 46 is 966.