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 730 the smallest integer that is 264260 that is divisible by both numbers.
Least Common Multiple (LCM) of 724 and 730 is 264260.
LCM(724,730) = 264260
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 730. First we will calculate the prime factors of 724 and 730.
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 730
2 | 730 |
5 | 365 |
73 | 73 |
1 |
Prime factors of 730 are 2, 5,73. Prime factorization of 730 in exponential form is:
730 = 21×51×731
Now multiplying the highest exponent prime factors to calculate the LCM of 724 and 730.
LCM(724,730) = 22×51×731×1811
LCM(724,730) = 264260
Factors of 724
List of positive integer factors of 724 that divides 724 without a remainder.
1, 2, 4, 181, 362, 724
Factors of 730
List of positive integer factors of 730 that divides 730 without a remainder.
1, 2, 5, 10, 73, 146, 365, 730
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 724 and 730, than apply into the LCM equation.
GCF(724,730) = 2
LCM(724,730) = ( 724 × 730) / 2
LCM(724,730) = 528520 / 2
LCM(724,730) = 264260
(i) The LCM of 730 and 724 is associative
LCM of 724 and 730 = LCM of 730 and 724
1. What is the LCM of 724 and 730?
Answer: LCM of 724 and 730 is 264260.
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 730?
Answer: Factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730. There are 8 integers that are factors of 730. The greatest factor of 730 is 730.
4. How to Find the LCM of 724 and 730?
Answer:
Least Common Multiple of 724 and 730 = 264260
Step 1: Find the prime factorization of 724
724 = 2 x 2 x 181
Step 2: Find the prime factorization of 730
730 = 2 x 5 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 264260 = 2 x 2 x 5 x 73 x 181
Step 4: Therefore, the least common multiple of 724 and 730 is 264260.