Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 654 and 662 the smallest integer that is 216474 that is divisible by both numbers.
Least Common Multiple (LCM) of 654 and 662 is 216474.
LCM(654,662) = 216474
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 654 and 662. First we will calculate the prime factors of 654 and 662.
Prime Factorization of 654
2 | 654 |
3 | 327 |
109 | 109 |
1 |
Prime factors of 654 are 2, 3,109. Prime factorization of 654 in exponential form is:
654 = 21×31×1091
Prime Factorization of 662
2 | 662 |
331 | 331 |
1 |
Prime factors of 662 are 2,331. Prime factorization of 662 in exponential form is:
662 = 21×3311
Now multiplying the highest exponent prime factors to calculate the LCM of 654 and 662.
LCM(654,662) = 21×31×1091×3311
LCM(654,662) = 216474
Factors of 654
List of positive integer factors of 654 that divides 654 without a remainder.
1, 2, 3, 6, 109, 218, 327, 654
Factors of 662
List of positive integer factors of 662 that divides 662 without a remainder.
1, 2, 331, 662
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 654 and 662, than apply into the LCM equation.
GCF(654,662) = 2
LCM(654,662) = ( 654 × 662) / 2
LCM(654,662) = 432948 / 2
LCM(654,662) = 216474
(i) The LCM of 662 and 654 is associative
LCM of 654 and 662 = LCM of 662 and 654
1. What is the LCM of 654 and 662?
Answer: LCM of 654 and 662 is 216474.
2. What are the Factors of 654?
Answer: Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654. There are 8 integers that are factors of 654. The greatest factor of 654 is 654.
3. What are the Factors of 662?
Answer: Factors of 662 are 1, 2, 331, 662. There are 4 integers that are factors of 662. The greatest factor of 662 is 662.
4. How to Find the LCM of 654 and 662?
Answer:
Least Common Multiple of 654 and 662 = 216474
Step 1: Find the prime factorization of 654
654 = 2 x 3 x 109
Step 2: Find the prime factorization of 662
662 = 2 x 331
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 216474 = 2 x 3 x 109 x 331
Step 4: Therefore, the least common multiple of 654 and 662 is 216474.