Least Common Multiple of 735 and 738
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 738 the smallest integer that is 180810 that is divisible by both numbers.
Least Common Multiple (LCM) of 735 and 738 is 180810.
LCM(735,738) = 180810
LCM of 735 and 738
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 735 and 738 by Prime method
- Least Common Multiple of 735 and 738 with GCF Formula
LCM of 735 and 738 is 180810
Least common multiple can be found by multiplying the highest exponent prime factors of 735 and 738. First we will calculate the prime factors of 735 and 738.
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 738
| 2 | 738 |
| 3 | 369 |
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 738 are 2, 3,41. Prime factorization of 738 in exponential form is:
738 = 21×32×411
Now multiplying the highest exponent prime factors to calculate the LCM of 735 and 738.
LCM(735,738) = 21×32×51×72×411
LCM(735,738) = 180810
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 738
List of positive integer factors of 738 that divides 738 without a remainder.
1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738
Least Common Multiple of 735 and 738 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 738, than apply into the LCM equation.
GCF(735,738) = 3
LCM(735,738) = ( 735 × 738) / 3
LCM(735,738) = 542430 / 3
LCM(735,738) = 180810
Properties of LCM 735 and 738
(i) The LCM of 738 and 735 is associative
LCM of 735 and 738 = LCM of 738 and 735
Related Least Common Multiples of 735
Related Least Common Multiples of 738
Frequently Asked Questions on LCM of 735 and 738
1. What is the LCM of 735 and 738?
Answer: LCM of 735 and 738 is 180810.
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 738?
Answer: Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738. There are 12 integers that are factors of 738. The greatest factor of 738 is 738.
4. How to Find the LCM of 735 and 738?
Answer:
Least Common Multiple of 735 and 738 = 180810
Step 1: Find the prime factorization of 735
735 = 3 x 5 x 7 x 7
Step 2: Find the prime factorization of 738
738 = 2 x 3 x 3 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 180810 = 2 x 3 x 3 x 5 x 7 x 7 x 41
Step 4: Therefore, the least common multiple of 735 and 738 is 180810.
