Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 731 and 736 the smallest integer that is 538016 that is divisible by both numbers.
Least Common Multiple (LCM) of 731 and 736 is 538016.
LCM(731,736) = 538016
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 731 and 736. First we will calculate the prime factors of 731 and 736.
Prime Factorization of 731
17 | 731 |
43 | 43 |
1 |
Prime factors of 731 are 17,43. Prime factorization of 731 in exponential form is:
731 = 171×431
Prime Factorization of 736
2 | 736 |
2 | 368 |
2 | 184 |
2 | 92 |
2 | 46 |
23 | 23 |
1 |
Prime factors of 736 are 2,23. Prime factorization of 736 in exponential form is:
736 = 25×231
Now multiplying the highest exponent prime factors to calculate the LCM of 731 and 736.
LCM(731,736) = 25×171×231×431
LCM(731,736) = 538016
Factors of 731
List of positive integer factors of 731 that divides 731 without a remainder.
1, 17, 43, 731
Factors of 736
List of positive integer factors of 736 that divides 736 without a remainder.
1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 731 and 736, than apply into the LCM equation.
GCF(731,736) = 1
LCM(731,736) = ( 731 × 736) / 1
LCM(731,736) = 538016 / 1
LCM(731,736) = 538016
(i) The LCM of 736 and 731 is associative
LCM of 731 and 736 = LCM of 736 and 731
1. What is the LCM of 731 and 736?
Answer: LCM of 731 and 736 is 538016.
2. What are the Factors of 731?
Answer: Factors of 731 are 1, 17, 43, 731. There are 4 integers that are factors of 731. The greatest factor of 731 is 731.
3. What are the Factors of 736?
Answer: Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736. There are 12 integers that are factors of 736. The greatest factor of 736 is 736.
4. How to Find the LCM of 731 and 736?
Answer:
Least Common Multiple of 731 and 736 = 538016
Step 1: Find the prime factorization of 731
731 = 17 x 43
Step 2: Find the prime factorization of 736
736 = 2 x 2 x 2 x 2 x 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 = 538016 = 2 x 2 x 2 x 2 x 2 x 17 x 23 x 43
Step 4: Therefore, the least common multiple of 731 and 736 is 538016.