Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2163 and 2164 the smallest integer that is 4680732 that is divisible by both numbers.
Least Common Multiple (LCM) of 2163 and 2164 is 4680732.
LCM(2163,2164) = 4680732
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 2163 and 2164. First we will calculate the prime factors of 2163 and 2164.
Prime Factorization of 2163
3 | 2163 |
7 | 721 |
103 | 103 |
1 |
Prime factors of 2163 are 3, 7,103. Prime factorization of 2163 in exponential form is:
2163 = 31×71×1031
Prime Factorization of 2164
2 | 2164 |
2 | 1082 |
541 | 541 |
1 |
Prime factors of 2164 are 2,541. Prime factorization of 2164 in exponential form is:
2164 = 22×5411
Now multiplying the highest exponent prime factors to calculate the LCM of 2163 and 2164.
LCM(2163,2164) = 22×31×71×1031×5411
LCM(2163,2164) = 4680732
Factors of 2163
List of positive integer factors of 2163 that divides 2163 without a remainder.
1, 3, 7, 21, 103, 309, 721, 2163
Factors of 2164
List of positive integer factors of 2164 that divides 2164 without a remainder.
1, 2, 4, 541, 1082, 2164
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2163 and 2164, than apply into the LCM equation.
GCF(2163,2164) = 1
LCM(2163,2164) = ( 2163 × 2164) / 1
LCM(2163,2164) = 4680732 / 1
LCM(2163,2164) = 4680732
(i) The LCM of 2164 and 2163 is associative
LCM of 2163 and 2164 = LCM of 2164 and 2163
1. What is the LCM of 2163 and 2164?
Answer: LCM of 2163 and 2164 is 4680732.
2. What are the Factors of 2163?
Answer: Factors of 2163 are 1, 3, 7, 21, 103, 309, 721, 2163. There are 8 integers that are factors of 2163. The greatest factor of 2163 is 2163.
3. What are the Factors of 2164?
Answer: Factors of 2164 are 1, 2, 4, 541, 1082, 2164. There are 6 integers that are factors of 2164. The greatest factor of 2164 is 2164.
4. How to Find the LCM of 2163 and 2164?
Answer:
Least Common Multiple of 2163 and 2164 = 4680732
Step 1: Find the prime factorization of 2163
2163 = 3 x 7 x 103
Step 2: Find the prime factorization of 2164
2164 = 2 x 2 x 541
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4680732 = 2 x 2 x 3 x 7 x 103 x 541
Step 4: Therefore, the least common multiple of 2163 and 2164 is 4680732.