Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 832 and 840 the smallest integer that is 87360 that is divisible by both numbers.
Least Common Multiple (LCM) of 832 and 840 is 87360.
LCM(832,840) = 87360
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 832 and 840. First we will calculate the prime factors of 832 and 840.
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
Prime Factorization of 840
2 | 840 |
2 | 420 |
2 | 210 |
3 | 105 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 840 are 2, 3, 5,7. Prime factorization of 840 in exponential form is:
840 = 23×31×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 832 and 840.
LCM(832,840) = 26×31×51×71×131
LCM(832,840) = 87360
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
Factors of 840
List of positive integer factors of 840 that divides 840 without a remainder.
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 832 and 840, than apply into the LCM equation.
GCF(832,840) = 8
LCM(832,840) = ( 832 × 840) / 8
LCM(832,840) = 698880 / 8
LCM(832,840) = 87360
(i) The LCM of 840 and 832 is associative
LCM of 832 and 840 = LCM of 840 and 832
1. What is the LCM of 832 and 840?
Answer: LCM of 832 and 840 is 87360.
2. 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.
3. What are the Factors of 840?
Answer: Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. There are 32 integers that are factors of 840. The greatest factor of 840 is 840.
4. How to Find the LCM of 832 and 840?
Answer:
Least Common Multiple of 832 and 840 = 87360
Step 1: Find the prime factorization of 832
832 = 2 x 2 x 2 x 2 x 2 x 2 x 13
Step 2: Find the prime factorization of 840
840 = 2 x 2 x 2 x 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 87360 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 13
Step 4: Therefore, the least common multiple of 832 and 840 is 87360.