Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 411 and 416 the smallest integer that is 170976 that is divisible by both numbers.
Least Common Multiple (LCM) of 411 and 416 is 170976.
LCM(411,416) = 170976
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 411 and 416. First we will calculate the prime factors of 411 and 416.
Prime Factorization of 411
3 | 411 |
137 | 137 |
1 |
Prime factors of 411 are 3,137. Prime factorization of 411 in exponential form is:
411 = 31×1371
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
Now multiplying the highest exponent prime factors to calculate the LCM of 411 and 416.
LCM(411,416) = 25×31×131×1371
LCM(411,416) = 170976
Factors of 411
List of positive integer factors of 411 that divides 411 without a remainder.
1, 3, 137, 411
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 411 and 416, than apply into the LCM equation.
GCF(411,416) = 1
LCM(411,416) = ( 411 × 416) / 1
LCM(411,416) = 170976 / 1
LCM(411,416) = 170976
(i) The LCM of 416 and 411 is associative
LCM of 411 and 416 = LCM of 416 and 411
1. What is the LCM of 411 and 416?
Answer: LCM of 411 and 416 is 170976.
2. What are the Factors of 411?
Answer: Factors of 411 are 1, 3, 137, 411. There are 4 integers that are factors of 411. The greatest factor of 411 is 411.
3. 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.
4. How to Find the LCM of 411 and 416?
Answer:
Least Common Multiple of 411 and 416 = 170976
Step 1: Find the prime factorization of 411
411 = 3 x 137
Step 2: Find the prime factorization of 416
416 = 2 x 2 x 2 x 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 170976 = 2 x 2 x 2 x 2 x 2 x 3 x 13 x 137
Step 4: Therefore, the least common multiple of 411 and 416 is 170976.