Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 624 and 632 the smallest integer that is 49296 that is divisible by both numbers.
Least Common Multiple (LCM) of 624 and 632 is 49296.
LCM(624,632) = 49296
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 624 and 632. First we will calculate the prime factors of 624 and 632.
Prime Factorization of 624
2 | 624 |
2 | 312 |
2 | 156 |
2 | 78 |
3 | 39 |
13 | 13 |
1 |
Prime factors of 624 are 2, 3,13. Prime factorization of 624 in exponential form is:
624 = 24×31×131
Prime Factorization of 632
2 | 632 |
2 | 316 |
2 | 158 |
79 | 79 |
1 |
Prime factors of 632 are 2,79. Prime factorization of 632 in exponential form is:
632 = 23×791
Now multiplying the highest exponent prime factors to calculate the LCM of 624 and 632.
LCM(624,632) = 24×31×131×791
LCM(624,632) = 49296
Factors of 624
List of positive integer factors of 624 that divides 624 without a remainder.
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
Factors of 632
List of positive integer factors of 632 that divides 632 without a remainder.
1, 2, 4, 8, 79, 158, 316, 632
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 624 and 632, than apply into the LCM equation.
GCF(624,632) = 8
LCM(624,632) = ( 624 × 632) / 8
LCM(624,632) = 394368 / 8
LCM(624,632) = 49296
(i) The LCM of 632 and 624 is associative
LCM of 624 and 632 = LCM of 632 and 624
1. What is the LCM of 624 and 632?
Answer: LCM of 624 and 632 is 49296.
2. What are the Factors of 624?
Answer: Factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624. There are 20 integers that are factors of 624. The greatest factor of 624 is 624.
3. What are the Factors of 632?
Answer: Factors of 632 are 1, 2, 4, 8, 79, 158, 316, 632. There are 8 integers that are factors of 632. The greatest factor of 632 is 632.
4. How to Find the LCM of 624 and 632?
Answer:
Least Common Multiple of 624 and 632 = 49296
Step 1: Find the prime factorization of 624
624 = 2 x 2 x 2 x 2 x 3 x 13
Step 2: Find the prime factorization of 632
632 = 2 x 2 x 2 x 79
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 49296 = 2 x 2 x 2 x 2 x 3 x 13 x 79
Step 4: Therefore, the least common multiple of 624 and 632 is 49296.