Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 416 and 423 the smallest integer that is 175968 that is divisible by both numbers.
Least Common Multiple (LCM) of 416 and 423 is 175968.
LCM(416,423) = 175968
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 416 and 423. First we will calculate the prime factors of 416 and 423.
Prime Factorization of 416
2 | 416 |
2 | 208 |
2 | 104 |
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 416 are 2,13. Prime factorization of 416 in exponential form is:
416 = 25×131
Prime Factorization of 423
3 | 423 |
3 | 141 |
47 | 47 |
1 |
Prime factors of 423 are 3,47. Prime factorization of 423 in exponential form is:
423 = 32×471
Now multiplying the highest exponent prime factors to calculate the LCM of 416 and 423.
LCM(416,423) = 25×32×131×471
LCM(416,423) = 175968
Factors of 416
List of positive integer factors of 416 that divides 416 without a remainder.
1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
Factors of 423
List of positive integer factors of 423 that divides 423 without a remainder.
1, 3, 9, 47, 141, 423
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 416 and 423, than apply into the LCM equation.
GCF(416,423) = 1
LCM(416,423) = ( 416 × 423) / 1
LCM(416,423) = 175968 / 1
LCM(416,423) = 175968
(i) The LCM of 423 and 416 is associative
LCM of 416 and 423 = LCM of 423 and 416
1. What is the LCM of 416 and 423?
Answer: LCM of 416 and 423 is 175968.
2. What are the Factors of 416?
Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.
3. What are the Factors of 423?
Answer: Factors of 423 are 1, 3, 9, 47, 141, 423. There are 6 integers that are factors of 423. The greatest factor of 423 is 423.
4. How to Find the LCM of 416 and 423?
Answer:
Least Common Multiple of 416 and 423 = 175968
Step 1: Find the prime factorization of 416
416 = 2 x 2 x 2 x 2 x 2 x 13
Step 2: Find the prime factorization of 423
423 = 3 x 3 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 175968 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 47
Step 4: Therefore, the least common multiple of 416 and 423 is 175968.