Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2169 and 2172 the smallest integer that is 1570356 that is divisible by both numbers.
Least Common Multiple (LCM) of 2169 and 2172 is 1570356.
LCM(2169,2172) = 1570356
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 2169 and 2172. First we will calculate the prime factors of 2169 and 2172.
Prime Factorization of 2169
3 | 2169 |
3 | 723 |
241 | 241 |
1 |
Prime factors of 2169 are 3,241. Prime factorization of 2169 in exponential form is:
2169 = 32×2411
Prime Factorization of 2172
2 | 2172 |
2 | 1086 |
3 | 543 |
181 | 181 |
1 |
Prime factors of 2172 are 2, 3,181. Prime factorization of 2172 in exponential form is:
2172 = 22×31×1811
Now multiplying the highest exponent prime factors to calculate the LCM of 2169 and 2172.
LCM(2169,2172) = 22×32×1811×2411
LCM(2169,2172) = 1570356
Factors of 2169
List of positive integer factors of 2169 that divides 2169 without a remainder.
1, 3, 9, 241, 723, 2169
Factors of 2172
List of positive integer factors of 2172 that divides 2172 without a remainder.
1, 2, 3, 4, 6, 12, 181, 362, 543, 724, 1086, 2172
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2169 and 2172, than apply into the LCM equation.
GCF(2169,2172) = 3
LCM(2169,2172) = ( 2169 × 2172) / 3
LCM(2169,2172) = 4711068 / 3
LCM(2169,2172) = 1570356
(i) The LCM of 2172 and 2169 is associative
LCM of 2169 and 2172 = LCM of 2172 and 2169
1. What is the LCM of 2169 and 2172?
Answer: LCM of 2169 and 2172 is 1570356.
2. What are the Factors of 2169?
Answer: Factors of 2169 are 1, 3, 9, 241, 723, 2169. There are 6 integers that are factors of 2169. The greatest factor of 2169 is 2169.
3. What are the Factors of 2172?
Answer: Factors of 2172 are 1, 2, 3, 4, 6, 12, 181, 362, 543, 724, 1086, 2172. There are 12 integers that are factors of 2172. The greatest factor of 2172 is 2172.
4. How to Find the LCM of 2169 and 2172?
Answer:
Least Common Multiple of 2169 and 2172 = 1570356
Step 1: Find the prime factorization of 2169
2169 = 3 x 3 x 241
Step 2: Find the prime factorization of 2172
2172 = 2 x 2 x 3 x 181
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1570356 = 2 x 2 x 3 x 3 x 181 x 241
Step 4: Therefore, the least common multiple of 2169 and 2172 is 1570356.