Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 724 and 729 the smallest integer that is 527796 that is divisible by both numbers.
Least Common Multiple (LCM) of 724 and 729 is 527796.
LCM(724,729) = 527796
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 724 and 729. First we will calculate the prime factors of 724 and 729.
Prime Factorization of 724
2 | 724 |
2 | 362 |
181 | 181 |
1 |
Prime factors of 724 are 2,181. Prime factorization of 724 in exponential form is:
724 = 22×1811
Prime Factorization of 729
3 | 729 |
3 | 243 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 729 are 3. Prime factorization of 729 in exponential form is:
729 = 36
Now multiplying the highest exponent prime factors to calculate the LCM of 724 and 729.
LCM(724,729) = 22×36×1811
LCM(724,729) = 527796
Factors of 724
List of positive integer factors of 724 that divides 724 without a remainder.
1, 2, 4, 181, 362, 724
Factors of 729
List of positive integer factors of 729 that divides 729 without a remainder.
1, 3, 9, 27, 81, 243, 729
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 724 and 729, than apply into the LCM equation.
GCF(724,729) = 1
LCM(724,729) = ( 724 × 729) / 1
LCM(724,729) = 527796 / 1
LCM(724,729) = 527796
(i) The LCM of 729 and 724 is associative
LCM of 724 and 729 = LCM of 729 and 724
1. What is the LCM of 724 and 729?
Answer: LCM of 724 and 729 is 527796.
2. What are the Factors of 724?
Answer: Factors of 724 are 1, 2, 4, 181, 362, 724. There are 6 integers that are factors of 724. The greatest factor of 724 is 724.
3. What are the Factors of 729?
Answer: Factors of 729 are 1, 3, 9, 27, 81, 243, 729. There are 7 integers that are factors of 729. The greatest factor of 729 is 729.
4. How to Find the LCM of 724 and 729?
Answer:
Least Common Multiple of 724 and 729 = 527796
Step 1: Find the prime factorization of 724
724 = 2 x 2 x 181
Step 2: Find the prime factorization of 729
729 = 3 x 3 x 3 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 527796 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 181
Step 4: Therefore, the least common multiple of 724 and 729 is 527796.