Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 745 and 752 the smallest integer that is 560240 that is divisible by both numbers.
Least Common Multiple (LCM) of 745 and 752 is 560240.
LCM(745,752) = 560240
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 745 and 752. First we will calculate the prime factors of 745 and 752.
Prime Factorization of 745
5 | 745 |
149 | 149 |
1 |
Prime factors of 745 are 5,149. Prime factorization of 745 in exponential form is:
745 = 51×1491
Prime Factorization of 752
2 | 752 |
2 | 376 |
2 | 188 |
2 | 94 |
47 | 47 |
1 |
Prime factors of 752 are 2,47. Prime factorization of 752 in exponential form is:
752 = 24×471
Now multiplying the highest exponent prime factors to calculate the LCM of 745 and 752.
LCM(745,752) = 24×51×471×1491
LCM(745,752) = 560240
Factors of 745
List of positive integer factors of 745 that divides 745 without a remainder.
1, 5, 149, 745
Factors of 752
List of positive integer factors of 752 that divides 752 without a remainder.
1, 2, 4, 8, 16, 47, 94, 188, 376, 752
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 745 and 752, than apply into the LCM equation.
GCF(745,752) = 1
LCM(745,752) = ( 745 × 752) / 1
LCM(745,752) = 560240 / 1
LCM(745,752) = 560240
(i) The LCM of 752 and 745 is associative
LCM of 745 and 752 = LCM of 752 and 745
1. What is the LCM of 745 and 752?
Answer: LCM of 745 and 752 is 560240.
2. What are the Factors of 745?
Answer: Factors of 745 are 1, 5, 149, 745. There are 4 integers that are factors of 745. The greatest factor of 745 is 745.
3. What are the Factors of 752?
Answer: Factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752. There are 10 integers that are factors of 752. The greatest factor of 752 is 752.
4. How to Find the LCM of 745 and 752?
Answer:
Least Common Multiple of 745 and 752 = 560240
Step 1: Find the prime factorization of 745
745 = 5 x 149
Step 2: Find the prime factorization of 752
752 = 2 x 2 x 2 x 2 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 560240 = 2 x 2 x 2 x 2 x 5 x 47 x 149
Step 4: Therefore, the least common multiple of 745 and 752 is 560240.