Least Common Multiple of 735 and 742
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 735 and 742 the smallest integer that is 77910 that is divisible by both numbers.
Least Common Multiple (LCM) of 735 and 742 is 77910.
LCM(735,742) = 77910
LCM of 735 and 742
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 735 and 742 by Prime method
- Least Common Multiple of 735 and 742 with GCF Formula
LCM of 735 and 742 is 77910
Least common multiple can be found by multiplying the highest exponent prime factors of 735 and 742. First we will calculate the prime factors of 735 and 742.
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
Prime Factorization of 742
| 2 | 742 |
| 7 | 371 |
| 53 | 53 |
| 1 |
Prime factors of 742 are 2, 7,53. Prime factorization of 742 in exponential form is:
742 = 21×71×531
Now multiplying the highest exponent prime factors to calculate the LCM of 735 and 742.
LCM(735,742) = 21×31×51×72×531
LCM(735,742) = 77910
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
Factors of 742
List of positive integer factors of 742 that divides 742 without a remainder.
1, 2, 7, 14, 53, 106, 371, 742
Least Common Multiple of 735 and 742 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 735 and 742, than apply into the LCM equation.
GCF(735,742) = 7
LCM(735,742) = ( 735 × 742) / 7
LCM(735,742) = 545370 / 7
LCM(735,742) = 77910
Properties of LCM 735 and 742
(i) The LCM of 742 and 735 is associative
LCM of 735 and 742 = LCM of 742 and 735
Related Least Common Multiples of 735
Related Least Common Multiples of 742
Frequently Asked Questions on LCM of 735 and 742
1. What is the LCM of 735 and 742?
Answer: LCM of 735 and 742 is 77910.
2. 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.
3. What are the Factors of 742?
Answer: Factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742. There are 8 integers that are factors of 742. The greatest factor of 742 is 742.
4. How to Find the LCM of 735 and 742?
Answer:
Least Common Multiple of 735 and 742 = 77910
Step 1: Find the prime factorization of 735
735 = 3 x 5 x 7 x 7
Step 2: Find the prime factorization of 742
742 = 2 x 7 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 77910 = 2 x 3 x 5 x 7 x 7 x 53
Step 4: Therefore, the least common multiple of 735 and 742 is 77910.