Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 742 and 746 the smallest integer that is 276766 that is divisible by both numbers.
Least Common Multiple (LCM) of 742 and 746 is 276766.
LCM(742,746) = 276766
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 742 and 746. First we will calculate the prime factors of 742 and 746.
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
Prime Factorization of 746
2 | 746 |
373 | 373 |
1 |
Prime factors of 746 are 2,373. Prime factorization of 746 in exponential form is:
746 = 21×3731
Now multiplying the highest exponent prime factors to calculate the LCM of 742 and 746.
LCM(742,746) = 21×71×531×3731
LCM(742,746) = 276766
Factors of 742
List of positive integer factors of 742 that divides 742 without a remainder.
1, 2, 7, 14, 53, 106, 371, 742
Factors of 746
List of positive integer factors of 746 that divides 746 without a remainder.
1, 2, 373, 746
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 742 and 746, than apply into the LCM equation.
GCF(742,746) = 2
LCM(742,746) = ( 742 × 746) / 2
LCM(742,746) = 553532 / 2
LCM(742,746) = 276766
(i) The LCM of 746 and 742 is associative
LCM of 742 and 746 = LCM of 746 and 742
1. What is the LCM of 742 and 746?
Answer: LCM of 742 and 746 is 276766.
2. 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.
3. What are the Factors of 746?
Answer: Factors of 746 are 1, 2, 373, 746. There are 4 integers that are factors of 746. The greatest factor of 746 is 746.
4. How to Find the LCM of 742 and 746?
Answer:
Least Common Multiple of 742 and 746 = 276766
Step 1: Find the prime factorization of 742
742 = 2 x 7 x 53
Step 2: Find the prime factorization of 746
746 = 2 x 373
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 276766 = 2 x 7 x 53 x 373
Step 4: Therefore, the least common multiple of 742 and 746 is 276766.