Least Common Multiple of 730 and 735
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 730 and 735 the smallest integer that is 107310 that is divisible by both numbers.
Least Common Multiple (LCM) of 730 and 735 is 107310.
LCM(730,735) = 107310
LCM of 730 and 735
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 730 and 735 by Prime method
- Least Common Multiple of 730 and 735 with GCF Formula
LCM of 730 and 735 is 107310
Least common multiple can be found by multiplying the highest exponent prime factors of 730 and 735. First we will calculate the prime factors of 730 and 735.
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
Prime Factorization of 735
| 3 | 735 |
| 5 | 245 |
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 735 are 3, 5,7. Prime factorization of 735 in exponential form is:
735 = 31×51×72
Now multiplying the highest exponent prime factors to calculate the LCM of 730 and 735.
LCM(730,735) = 21×31×51×72×731
LCM(730,735) = 107310
Factors of 730
List of positive integer factors of 730 that divides 730 without a remainder.
1, 2, 5, 10, 73, 146, 365, 730
Factors of 735
List of positive integer factors of 735 that divides 735 without a remainder.
1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
Least Common Multiple of 730 and 735 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 730 and 735, than apply into the LCM equation.
GCF(730,735) = 5
LCM(730,735) = ( 730 × 735) / 5
LCM(730,735) = 536550 / 5
LCM(730,735) = 107310
Properties of LCM 730 and 735
(i) The LCM of 735 and 730 is associative
LCM of 730 and 735 = LCM of 735 and 730
Related Least Common Multiples of 730
Related Least Common Multiples of 735
Frequently Asked Questions on LCM of 730 and 735
1. What is the LCM of 730 and 735?
Answer: LCM of 730 and 735 is 107310.
2. 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.
3. What are the Factors of 735?
Answer: Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. There are 12 integers that are factors of 735. The greatest factor of 735 is 735.
4. How to Find the LCM of 730 and 735?
Answer:
Least Common Multiple of 730 and 735 = 107310
Step 1: Find the prime factorization of 730
730 = 2 x 5 x 73
Step 2: Find the prime factorization of 735
735 = 3 x 5 x 7 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 = 107310 = 2 x 3 x 5 x 7 x 7 x 73
Step 4: Therefore, the least common multiple of 730 and 735 is 107310.