Least Common Multiple of 49 and 56
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 49 and 56 the smallest integer that is 392 that is divisible by both numbers.
Least Common Multiple (LCM) of 49 and 56 is 392.
LCM(49,56) = 392
LCM of 49 and 56
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 49 and 56 by Prime method
- Least Common Multiple of 49 and 56 with GCF Formula
LCM of 49 and 56 is 392
Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 56. First we will calculate the prime factors of 49 and 56.
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
Prime Factorization of 56
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 56 are 2,7. Prime factorization of 56 in exponential form is:
56 = 23×71
Now multiplying the highest exponent prime factors to calculate the LCM of 49 and 56.
LCM(49,56) = 23×72
LCM(49,56) = 392
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1, 7, 49
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1, 2, 4, 7, 8, 14, 28, 56
Least Common Multiple of 49 and 56 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 56, than apply into the LCM equation.
GCF(49,56) = 7
LCM(49,56) = ( 49 × 56) / 7
LCM(49,56) = 2744 / 7
LCM(49,56) = 392
Properties of LCM 49 and 56
(i) The LCM of 56 and 49 is associative
LCM of 49 and 56 = LCM of 56 and 49
Related Least Common Multiples of 49
Related Least Common Multiples of 56
Frequently Asked Questions on LCM of 49 and 56
1. What is the LCM of 49 and 56?
Answer: LCM of 49 and 56 is 392.
2. 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.
3. What are the Factors of 56?
Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.
4. How to Find the LCM of 49 and 56?
Answer:
Least Common Multiple of 49 and 56 = 392
Step 1: Find the prime factorization of 49
49 = 7 x 7
Step 2: Find the prime factorization of 56
56 = 2 x 2 x 2 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 = 392 = 2 x 2 x 2 x 7 x 7
Step 4: Therefore, the least common multiple of 49 and 56 is 392.