Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 729 and 734 the smallest integer that is 535086 that is divisible by both numbers.
Least Common Multiple (LCM) of 729 and 734 is 535086.
LCM(729,734) = 535086
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 729 and 734. First we will calculate the prime factors of 729 and 734.
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
Prime Factorization of 734
2 | 734 |
367 | 367 |
1 |
Prime factors of 734 are 2,367. Prime factorization of 734 in exponential form is:
734 = 21×3671
Now multiplying the highest exponent prime factors to calculate the LCM of 729 and 734.
LCM(729,734) = 21×36×3671
LCM(729,734) = 535086
Factors of 729
List of positive integer factors of 729 that divides 729 without a remainder.
1, 3, 9, 27, 81, 243, 729
Factors of 734
List of positive integer factors of 734 that divides 734 without a remainder.
1, 2, 367, 734
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 729 and 734, than apply into the LCM equation.
GCF(729,734) = 1
LCM(729,734) = ( 729 × 734) / 1
LCM(729,734) = 535086 / 1
LCM(729,734) = 535086
(i) The LCM of 734 and 729 is associative
LCM of 729 and 734 = LCM of 734 and 729
1. What is the LCM of 729 and 734?
Answer: LCM of 729 and 734 is 535086.
2. 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.
3. What are the Factors of 734?
Answer: Factors of 734 are 1, 2, 367, 734. There are 4 integers that are factors of 734. The greatest factor of 734 is 734.
4. How to Find the LCM of 729 and 734?
Answer:
Least Common Multiple of 729 and 734 = 535086
Step 1: Find the prime factorization of 729
729 = 3 x 3 x 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 734
734 = 2 x 367
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 535086 = 2 x 3 x 3 x 3 x 3 x 3 x 3 x 367
Step 4: Therefore, the least common multiple of 729 and 734 is 535086.