Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 726 and 732 the smallest integer that is 88572 that is divisible by both numbers.
Least Common Multiple (LCM) of 726 and 732 is 88572.
LCM(726,732) = 88572
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 726 and 732. First we will calculate the prime factors of 726 and 732.
Prime Factorization of 726
2 | 726 |
3 | 363 |
11 | 121 |
11 | 11 |
1 |
Prime factors of 726 are 2, 3,11. Prime factorization of 726 in exponential form is:
726 = 21×31×112
Prime Factorization of 732
2 | 732 |
2 | 366 |
3 | 183 |
61 | 61 |
1 |
Prime factors of 732 are 2, 3,61. Prime factorization of 732 in exponential form is:
732 = 22×31×611
Now multiplying the highest exponent prime factors to calculate the LCM of 726 and 732.
LCM(726,732) = 22×31×112×611
LCM(726,732) = 88572
Factors of 726
List of positive integer factors of 726 that divides 726 without a remainder.
1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726
Factors of 732
List of positive integer factors of 732 that divides 732 without a remainder.
1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 726 and 732, than apply into the LCM equation.
GCF(726,732) = 6
LCM(726,732) = ( 726 × 732) / 6
LCM(726,732) = 531432 / 6
LCM(726,732) = 88572
(i) The LCM of 732 and 726 is associative
LCM of 726 and 732 = LCM of 732 and 726
1. What is the LCM of 726 and 732?
Answer: LCM of 726 and 732 is 88572.
2. What are the Factors of 726?
Answer: Factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726. There are 12 integers that are factors of 726. The greatest factor of 726 is 726.
3. What are the Factors of 732?
Answer: Factors of 732 are 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732. There are 12 integers that are factors of 732. The greatest factor of 732 is 732.
4. How to Find the LCM of 726 and 732?
Answer:
Least Common Multiple of 726 and 732 = 88572
Step 1: Find the prime factorization of 726
726 = 2 x 3 x 11 x 11
Step 2: Find the prime factorization of 732
732 = 2 x 2 x 3 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 88572 = 2 x 2 x 3 x 11 x 11 x 61
Step 4: Therefore, the least common multiple of 726 and 732 is 88572.