Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 740 and 746 the smallest integer that is 276020 that is divisible by both numbers.
Least Common Multiple (LCM) of 740 and 746 is 276020.
LCM(740,746) = 276020
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 740 and 746. First we will calculate the prime factors of 740 and 746.
Prime Factorization of 740
2 | 740 |
2 | 370 |
5 | 185 |
37 | 37 |
1 |
Prime factors of 740 are 2, 5,37. Prime factorization of 740 in exponential form is:
740 = 22×51×371
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 740 and 746.
LCM(740,746) = 22×51×371×3731
LCM(740,746) = 276020
Factors of 740
List of positive integer factors of 740 that divides 740 without a remainder.
1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740
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 740 and 746, than apply into the LCM equation.
GCF(740,746) = 2
LCM(740,746) = ( 740 × 746) / 2
LCM(740,746) = 552040 / 2
LCM(740,746) = 276020
(i) The LCM of 746 and 740 is associative
LCM of 740 and 746 = LCM of 746 and 740
1. What is the LCM of 740 and 746?
Answer: LCM of 740 and 746 is 276020.
2. What are the Factors of 740?
Answer: Factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740. There are 12 integers that are factors of 740. The greatest factor of 740 is 740.
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 740 and 746?
Answer:
Least Common Multiple of 740 and 746 = 276020
Step 1: Find the prime factorization of 740
740 = 2 x 2 x 5 x 37
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 = 276020 = 2 x 2 x 5 x 37 x 373
Step 4: Therefore, the least common multiple of 740 and 746 is 276020.