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 833 the smallest integer that is 689724 that is divisible by both numbers.
Least Common Multiple (LCM) of 828 and 833 is 689724.
LCM(828,833) = 689724
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 833. First we will calculate the prime factors of 828 and 833.
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 833
7 | 833 |
7 | 119 |
17 | 17 |
1 |
Prime factors of 833 are 7,17. Prime factorization of 833 in exponential form is:
833 = 72×171
Now multiplying the highest exponent prime factors to calculate the LCM of 828 and 833.
LCM(828,833) = 22×32×72×171×231
LCM(828,833) = 689724
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 833
List of positive integer factors of 833 that divides 833 without a remainder.
1, 7, 17, 49, 119, 833
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 828 and 833, than apply into the LCM equation.
GCF(828,833) = 1
LCM(828,833) = ( 828 × 833) / 1
LCM(828,833) = 689724 / 1
LCM(828,833) = 689724
(i) The LCM of 833 and 828 is associative
LCM of 828 and 833 = LCM of 833 and 828
1. What is the LCM of 828 and 833?
Answer: LCM of 828 and 833 is 689724.
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 833?
Answer: Factors of 833 are 1, 7, 17, 49, 119, 833. There are 6 integers that are factors of 833. The greatest factor of 833 is 833.
4. How to Find the LCM of 828 and 833?
Answer:
Least Common Multiple of 828 and 833 = 689724
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 833
833 = 7 x 7 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 689724 = 2 x 2 x 3 x 3 x 7 x 7 x 17 x 23
Step 4: Therefore, the least common multiple of 828 and 833 is 689724.