Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1675 and 1680 the smallest integer that is 562800 that is divisible by both numbers.
Least Common Multiple (LCM) of 1675 and 1680 is 562800.
LCM(1675,1680) = 562800
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 1675 and 1680. First we will calculate the prime factors of 1675 and 1680.
Prime Factorization of 1675
5 | 1675 |
5 | 335 |
67 | 67 |
1 |
Prime factors of 1675 are 5,67. Prime factorization of 1675 in exponential form is:
1675 = 52×671
Prime Factorization of 1680
2 | 1680 |
2 | 840 |
2 | 420 |
2 | 210 |
3 | 105 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 1680 are 2, 3, 5,7. Prime factorization of 1680 in exponential form is:
1680 = 24×31×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 1675 and 1680.
LCM(1675,1680) = 24×31×52×71×671
LCM(1675,1680) = 562800
Factors of 1675
List of positive integer factors of 1675 that divides 1675 without a remainder.
1, 5, 25, 67, 335, 1675
Factors of 1680
List of positive integer factors of 1680 that divides 1680 without a remainder.
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1675 and 1680, than apply into the LCM equation.
GCF(1675,1680) = 5
LCM(1675,1680) = ( 1675 × 1680) / 5
LCM(1675,1680) = 2814000 / 5
LCM(1675,1680) = 562800
(i) The LCM of 1680 and 1675 is associative
LCM of 1675 and 1680 = LCM of 1680 and 1675
1. What is the LCM of 1675 and 1680?
Answer: LCM of 1675 and 1680 is 562800.
2. What are the Factors of 1675?
Answer: Factors of 1675 are 1, 5, 25, 67, 335, 1675. There are 6 integers that are factors of 1675. The greatest factor of 1675 is 1675.
3. What are the Factors of 1680?
Answer: Factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680. There are 40 integers that are factors of 1680. The greatest factor of 1680 is 1680.
4. How to Find the LCM of 1675 and 1680?
Answer:
Least Common Multiple of 1675 and 1680 = 562800
Step 1: Find the prime factorization of 1675
1675 = 5 x 5 x 67
Step 2: Find the prime factorization of 1680
1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 562800 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 67
Step 4: Therefore, the least common multiple of 1675 and 1680 is 562800.