Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1658 and 1664 the smallest integer that is 1379456 that is divisible by both numbers.
Least Common Multiple (LCM) of 1658 and 1664 is 1379456.
LCM(1658,1664) = 1379456
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 1658 and 1664. First we will calculate the prime factors of 1658 and 1664.
Prime Factorization of 1658
2 | 1658 |
829 | 829 |
1 |
Prime factors of 1658 are 2,829. Prime factorization of 1658 in exponential form is:
1658 = 21×8291
Prime Factorization of 1664
2 | 1664 |
2 | 832 |
2 | 416 |
2 | 208 |
2 | 104 |
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 1664 are 2,13. Prime factorization of 1664 in exponential form is:
1664 = 27×131
Now multiplying the highest exponent prime factors to calculate the LCM of 1658 and 1664.
LCM(1658,1664) = 27×131×8291
LCM(1658,1664) = 1379456
Factors of 1658
List of positive integer factors of 1658 that divides 1658 without a remainder.
1, 2, 829, 1658
Factors of 1664
List of positive integer factors of 1664 that divides 1664 without a remainder.
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1658 and 1664, than apply into the LCM equation.
GCF(1658,1664) = 2
LCM(1658,1664) = ( 1658 × 1664) / 2
LCM(1658,1664) = 2758912 / 2
LCM(1658,1664) = 1379456
(i) The LCM of 1664 and 1658 is associative
LCM of 1658 and 1664 = LCM of 1664 and 1658
1. What is the LCM of 1658 and 1664?
Answer: LCM of 1658 and 1664 is 1379456.
2. What are the Factors of 1658?
Answer: Factors of 1658 are 1, 2, 829, 1658. There are 4 integers that are factors of 1658. The greatest factor of 1658 is 1658.
3. What are the Factors of 1664?
Answer: Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664. There are 16 integers that are factors of 1664. The greatest factor of 1664 is 1664.
4. How to Find the LCM of 1658 and 1664?
Answer:
Least Common Multiple of 1658 and 1664 = 1379456
Step 1: Find the prime factorization of 1658
1658 = 2 x 829
Step 2: Find the prime factorization of 1664
1664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1379456 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13 x 829
Step 4: Therefore, the least common multiple of 1658 and 1664 is 1379456.