Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 750 and 752 the smallest integer that is 282000 that is divisible by both numbers.
Least Common Multiple (LCM) of 750 and 752 is 282000.
LCM(750,752) = 282000
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 750 and 752. First we will calculate the prime factors of 750 and 752.
Prime Factorization of 750
2 | 750 |
3 | 375 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 750 are 2, 3,5. Prime factorization of 750 in exponential form is:
750 = 21×31×53
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 750 and 752.
LCM(750,752) = 24×31×53×471
LCM(750,752) = 282000
Factors of 750
List of positive integer factors of 750 that divides 750 without a remainder.
1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
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 750 and 752, than apply into the LCM equation.
GCF(750,752) = 2
LCM(750,752) = ( 750 × 752) / 2
LCM(750,752) = 564000 / 2
LCM(750,752) = 282000
(i) The LCM of 752 and 750 is associative
LCM of 750 and 752 = LCM of 752 and 750
1. What is the LCM of 750 and 752?
Answer: LCM of 750 and 752 is 282000.
2. What are the Factors of 750?
Answer: Factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750. There are 16 integers that are factors of 750. The greatest factor of 750 is 750.
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 750 and 752?
Answer:
Least Common Multiple of 750 and 752 = 282000
Step 1: Find the prime factorization of 750
750 = 2 x 3 x 5 x 5 x 5
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 = 282000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 47
Step 4: Therefore, the least common multiple of 750 and 752 is 282000.