Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1604 and 1605 the smallest integer that is 2574420 that is divisible by both numbers.
Least Common Multiple (LCM) of 1604 and 1605 is 2574420.
LCM(1604,1605) = 2574420
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 1604 and 1605. First we will calculate the prime factors of 1604 and 1605.
Prime Factorization of 1604
2 | 1604 |
2 | 802 |
401 | 401 |
1 |
Prime factors of 1604 are 2,401. Prime factorization of 1604 in exponential form is:
1604 = 22×4011
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
Now multiplying the highest exponent prime factors to calculate the LCM of 1604 and 1605.
LCM(1604,1605) = 22×31×51×1071×4011
LCM(1604,1605) = 2574420
Factors of 1604
List of positive integer factors of 1604 that divides 1604 without a remainder.
1, 2, 4, 401, 802, 1604
Factors of 1605
List of positive integer factors of 1605 that divides 1605 without a remainder.
1, 3, 5, 15, 107, 321, 535, 1605
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1604 and 1605, than apply into the LCM equation.
GCF(1604,1605) = 1
LCM(1604,1605) = ( 1604 × 1605) / 1
LCM(1604,1605) = 2574420 / 1
LCM(1604,1605) = 2574420
(i) The LCM of 1605 and 1604 is associative
LCM of 1604 and 1605 = LCM of 1605 and 1604
1. What is the LCM of 1604 and 1605?
Answer: LCM of 1604 and 1605 is 2574420.
2. What are the Factors of 1604?
Answer: Factors of 1604 are 1, 2, 4, 401, 802, 1604. There are 6 integers that are factors of 1604. The greatest factor of 1604 is 1604.
3. 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.
4. How to Find the LCM of 1604 and 1605?
Answer:
Least Common Multiple of 1604 and 1605 = 2574420
Step 1: Find the prime factorization of 1604
1604 = 2 x 2 x 401
Step 2: Find the prime factorization of 1605
1605 = 3 x 5 x 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2574420 = 2 x 2 x 3 x 5 x 107 x 401
Step 4: Therefore, the least common multiple of 1604 and 1605 is 2574420.