Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1605 and 1608 the smallest integer that is 860280 that is divisible by both numbers.
Least Common Multiple (LCM) of 1605 and 1608 is 860280.
LCM(1605,1608) = 860280
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 1605 and 1608. First we will calculate the prime factors of 1605 and 1608.
Prime Factorization of 1605
3 | 1605 |
5 | 535 |
107 | 107 |
1 |
Prime factors of 1605 are 3, 5,107. Prime factorization of 1605 in exponential form is:
1605 = 31×51×1071
Prime Factorization of 1608
2 | 1608 |
2 | 804 |
2 | 402 |
3 | 201 |
67 | 67 |
1 |
Prime factors of 1608 are 2, 3,67. Prime factorization of 1608 in exponential form is:
1608 = 23×31×671
Now multiplying the highest exponent prime factors to calculate the LCM of 1605 and 1608.
LCM(1605,1608) = 23×31×51×671×1071
LCM(1605,1608) = 860280
Factors of 1605
List of positive integer factors of 1605 that divides 1605 without a remainder.
1, 3, 5, 15, 107, 321, 535, 1605
Factors of 1608
List of positive integer factors of 1608 that divides 1608 without a remainder.
1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1605 and 1608, than apply into the LCM equation.
GCF(1605,1608) = 3
LCM(1605,1608) = ( 1605 × 1608) / 3
LCM(1605,1608) = 2580840 / 3
LCM(1605,1608) = 860280
(i) The LCM of 1608 and 1605 is associative
LCM of 1605 and 1608 = LCM of 1608 and 1605
1. What is the LCM of 1605 and 1608?
Answer: LCM of 1605 and 1608 is 860280.
2. What are the Factors of 1605?
Answer: Factors of 1605 are 1, 3, 5, 15, 107, 321, 535, 1605. There are 8 integers that are factors of 1605. The greatest factor of 1605 is 1605.
3. What are the Factors of 1608?
Answer: Factors of 1608 are 1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608. There are 16 integers that are factors of 1608. The greatest factor of 1608 is 1608.
4. How to Find the LCM of 1605 and 1608?
Answer:
Least Common Multiple of 1605 and 1608 = 860280
Step 1: Find the prime factorization of 1605
1605 = 3 x 5 x 107
Step 2: Find the prime factorization of 1608
1608 = 2 x 2 x 2 x 3 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 860280 = 2 x 2 x 2 x 3 x 5 x 67 x 107
Step 4: Therefore, the least common multiple of 1605 and 1608 is 860280.