Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 822 and 827 the smallest integer that is 679794 that is divisible by both numbers.
Least Common Multiple (LCM) of 822 and 827 is 679794.
LCM(822,827) = 679794
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 822 and 827. First we will calculate the prime factors of 822 and 827.
Prime Factorization of 822
2 | 822 |
3 | 411 |
137 | 137 |
1 |
Prime factors of 822 are 2, 3,137. Prime factorization of 822 in exponential form is:
822 = 21×31×1371
Prime Factorization of 827
827 | 827 |
1 |
Prime factors of 827 are 827. Prime factorization of 827 in exponential form is:
827 = 8271
Now multiplying the highest exponent prime factors to calculate the LCM of 822 and 827.
LCM(822,827) = 21×31×1371×8271
LCM(822,827) = 679794
Factors of 822
List of positive integer factors of 822 that divides 822 without a remainder.
1, 2, 3, 6, 137, 274, 411, 822
Factors of 827
List of positive integer factors of 827 that divides 827 without a remainder.
1, 827
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 822 and 827, than apply into the LCM equation.
GCF(822,827) = 1
LCM(822,827) = ( 822 × 827) / 1
LCM(822,827) = 679794 / 1
LCM(822,827) = 679794
(i) The LCM of 827 and 822 is associative
LCM of 822 and 827 = LCM of 827 and 822
1. What is the LCM of 822 and 827?
Answer: LCM of 822 and 827 is 679794.
2. What are the Factors of 822?
Answer: Factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822. There are 8 integers that are factors of 822. The greatest factor of 822 is 822.
3. What are the Factors of 827?
Answer: Factors of 827 are 1, 827. There are 2 integers that are factors of 827. The greatest factor of 827 is 827.
4. How to Find the LCM of 822 and 827?
Answer:
Least Common Multiple of 822 and 827 = 679794
Step 1: Find the prime factorization of 822
822 = 2 x 3 x 137
Step 2: Find the prime factorization of 827
827 = 827
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 679794 = 2 x 3 x 137 x 827
Step 4: Therefore, the least common multiple of 822 and 827 is 679794.