Least Common Multiple of 42 and 49
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 49 the smallest integer that is 294 that is divisible by both numbers.
Least Common Multiple (LCM) of 42 and 49 is 294.
LCM(42,49) = 294
LCM of 42 and 49
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 42 and 49 by Prime method
- Least Common Multiple of 42 and 49 with GCF Formula
LCM of 42 and 49 is 294
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 49. First we will calculate the prime factors of 42 and 49.
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 49
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:
49 = 72
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 49.
LCM(42,49) = 21×31×72
LCM(42,49) = 294
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 49
List of positive integer factors of 49 that divides 49 without a remainder.
1, 7, 49
Least Common Multiple of 42 and 49 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 49, than apply into the LCM equation.
GCF(42,49) = 7
LCM(42,49) = ( 42 × 49) / 7
LCM(42,49) = 2058 / 7
LCM(42,49) = 294
Properties of LCM 42 and 49
(i) The LCM of 49 and 42 is associative
LCM of 42 and 49 = LCM of 49 and 42
Related Least Common Multiples of 42
Related Least Common Multiples of 49
Frequently Asked Questions on LCM of 42 and 49
1. What is the LCM of 42 and 49?
Answer: LCM of 42 and 49 is 294.
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 49?
Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.
4. How to Find the LCM of 42 and 49?
Answer:
Least Common Multiple of 42 and 49 = 294
Step 1: Find the prime factorization of 42
42 = 2 x 3 x 7
Step 2: Find the prime factorization of 49
49 = 7 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 = 294 = 2 x 3 x 7 x 7
Step 4: Therefore, the least common multiple of 42 and 49 is 294.