Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 828 and 832 the smallest integer that is 172224 that is divisible by both numbers.
Least Common Multiple (LCM) of 828 and 832 is 172224.
LCM(828,832) = 172224
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 828 and 832. First we will calculate the prime factors of 828 and 832.
Prime Factorization of 828
2 | 828 |
2 | 414 |
3 | 207 |
3 | 69 |
23 | 23 |
1 |
Prime factors of 828 are 2, 3,23. Prime factorization of 828 in exponential form is:
828 = 22×32×231
Prime Factorization of 832
2 | 832 |
2 | 416 |
2 | 208 |
2 | 104 |
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 832 are 2,13. Prime factorization of 832 in exponential form is:
832 = 26×131
Now multiplying the highest exponent prime factors to calculate the LCM of 828 and 832.
LCM(828,832) = 26×32×131×231
LCM(828,832) = 172224
Factors of 828
List of positive integer factors of 828 that divides 828 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
Factors of 832
List of positive integer factors of 832 that divides 832 without a remainder.
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 828 and 832, than apply into the LCM equation.
GCF(828,832) = 4
LCM(828,832) = ( 828 × 832) / 4
LCM(828,832) = 688896 / 4
LCM(828,832) = 172224
(i) The LCM of 832 and 828 is associative
LCM of 828 and 832 = LCM of 832 and 828
1. What is the LCM of 828 and 832?
Answer: LCM of 828 and 832 is 172224.
2. What are the Factors of 828?
Answer: Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. There are 18 integers that are factors of 828. The greatest factor of 828 is 828.
3. What are the Factors of 832?
Answer: Factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832. There are 14 integers that are factors of 832. The greatest factor of 832 is 832.
4. How to Find the LCM of 828 and 832?
Answer:
Least Common Multiple of 828 and 832 = 172224
Step 1: Find the prime factorization of 828
828 = 2 x 2 x 3 x 3 x 23
Step 2: Find the prime factorization of 832
832 = 2 x 2 x 2 x 2 x 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 172224 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 23
Step 4: Therefore, the least common multiple of 828 and 832 is 172224.