Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 670 and 677 the smallest integer that is 453590 that is divisible by both numbers.
Least Common Multiple (LCM) of 670 and 677 is 453590.
LCM(670,677) = 453590
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 670 and 677. First we will calculate the prime factors of 670 and 677.
Prime Factorization of 670
2 | 670 |
5 | 335 |
67 | 67 |
1 |
Prime factors of 670 are 2, 5,67. Prime factorization of 670 in exponential form is:
670 = 21×51×671
Prime Factorization of 677
677 | 677 |
1 |
Prime factors of 677 are 677. Prime factorization of 677 in exponential form is:
677 = 6771
Now multiplying the highest exponent prime factors to calculate the LCM of 670 and 677.
LCM(670,677) = 21×51×671×6771
LCM(670,677) = 453590
Factors of 670
List of positive integer factors of 670 that divides 670 without a remainder.
1, 2, 5, 10, 67, 134, 335, 670
Factors of 677
List of positive integer factors of 677 that divides 677 without a remainder.
1, 677
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 670 and 677, than apply into the LCM equation.
GCF(670,677) = 1
LCM(670,677) = ( 670 × 677) / 1
LCM(670,677) = 453590 / 1
LCM(670,677) = 453590
(i) The LCM of 677 and 670 is associative
LCM of 670 and 677 = LCM of 677 and 670
1. What is the LCM of 670 and 677?
Answer: LCM of 670 and 677 is 453590.
2. What are the Factors of 670?
Answer: Factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670. There are 8 integers that are factors of 670. The greatest factor of 670 is 670.
3. What are the Factors of 677?
Answer: Factors of 677 are 1, 677. There are 2 integers that are factors of 677. The greatest factor of 677 is 677.
4. How to Find the LCM of 670 and 677?
Answer:
Least Common Multiple of 670 and 677 = 453590
Step 1: Find the prime factorization of 670
670 = 2 x 5 x 67
Step 2: Find the prime factorization of 677
677 = 677
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 453590 = 2 x 5 x 67 x 677
Step 4: Therefore, the least common multiple of 670 and 677 is 453590.