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 2170 the smallest integer that is 4706730 that is divisible by both numbers.
Least Common Multiple (LCM) of 2169 and 2170 is 4706730.
LCM(2169,2170) = 4706730
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 2170. First we will calculate the prime factors of 2169 and 2170.
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 2170
2 | 2170 |
5 | 1085 |
7 | 217 |
31 | 31 |
1 |
Prime factors of 2170 are 2, 5, 7,31. Prime factorization of 2170 in exponential form is:
2170 = 21×51×71×311
Now multiplying the highest exponent prime factors to calculate the LCM of 2169 and 2170.
LCM(2169,2170) = 21×32×51×71×311×2411
LCM(2169,2170) = 4706730
Factors of 2169
List of positive integer factors of 2169 that divides 2169 without a remainder.
1, 3, 9, 241, 723, 2169
Factors of 2170
List of positive integer factors of 2170 that divides 2170 without a remainder.
1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2169 and 2170, than apply into the LCM equation.
GCF(2169,2170) = 1
LCM(2169,2170) = ( 2169 × 2170) / 1
LCM(2169,2170) = 4706730 / 1
LCM(2169,2170) = 4706730
(i) The LCM of 2170 and 2169 is associative
LCM of 2169 and 2170 = LCM of 2170 and 2169
1. What is the LCM of 2169 and 2170?
Answer: LCM of 2169 and 2170 is 4706730.
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 2170?
Answer: Factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170. There are 16 integers that are factors of 2170. The greatest factor of 2170 is 2170.
4. How to Find the LCM of 2169 and 2170?
Answer:
Least Common Multiple of 2169 and 2170 = 4706730
Step 1: Find the prime factorization of 2169
2169 = 3 x 3 x 241
Step 2: Find the prime factorization of 2170
2170 = 2 x 5 x 7 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4706730 = 2 x 3 x 3 x 5 x 7 x 31 x 241
Step 4: Therefore, the least common multiple of 2169 and 2170 is 4706730.