Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8412 and 8416 the smallest integer that is 17698848 that is divisible by both numbers.
Least Common Multiple (LCM) of 8412 and 8416 is 17698848.
LCM(8412,8416) = 17698848
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 8412 and 8416. First we will calculate the prime factors of 8412 and 8416.
Prime Factorization of 8412
2 | 8412 |
2 | 4206 |
3 | 2103 |
701 | 701 |
1 |
Prime factors of 8412 are 2, 3,701. Prime factorization of 8412 in exponential form is:
8412 = 22×31×7011
Prime Factorization of 8416
2 | 8416 |
2 | 4208 |
2 | 2104 |
2 | 1052 |
2 | 526 |
263 | 263 |
1 |
Prime factors of 8416 are 2,263. Prime factorization of 8416 in exponential form is:
8416 = 25×2631
Now multiplying the highest exponent prime factors to calculate the LCM of 8412 and 8416.
LCM(8412,8416) = 25×31×2631×7011
LCM(8412,8416) = 17698848
Factors of 8412
List of positive integer factors of 8412 that divides 8412 without a remainder.
1, 2, 3, 4, 6, 12, 701, 1402, 2103, 2804, 4206, 8412
Factors of 8416
List of positive integer factors of 8416 that divides 8416 without a remainder.
1, 2, 4, 8, 16, 32, 263, 526, 1052, 2104, 4208, 8416
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8412 and 8416, than apply into the LCM equation.
GCF(8412,8416) = 4
LCM(8412,8416) = ( 8412 × 8416) / 4
LCM(8412,8416) = 70795392 / 4
LCM(8412,8416) = 17698848
(i) The LCM of 8416 and 8412 is associative
LCM of 8412 and 8416 = LCM of 8416 and 8412
1. What is the LCM of 8412 and 8416?
Answer: LCM of 8412 and 8416 is 17698848.
2. What are the Factors of 8412?
Answer: Factors of 8412 are 1, 2, 3, 4, 6, 12, 701, 1402, 2103, 2804, 4206, 8412. There are 12 integers that are factors of 8412. The greatest factor of 8412 is 8412.
3. What are the Factors of 8416?
Answer: Factors of 8416 are 1, 2, 4, 8, 16, 32, 263, 526, 1052, 2104, 4208, 8416. There are 12 integers that are factors of 8416. The greatest factor of 8416 is 8416.
4. How to Find the LCM of 8412 and 8416?
Answer:
Least Common Multiple of 8412 and 8416 = 17698848
Step 1: Find the prime factorization of 8412
8412 = 2 x 2 x 3 x 701
Step 2: Find the prime factorization of 8416
8416 = 2 x 2 x 2 x 2 x 2 x 263
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 17698848 = 2 x 2 x 2 x 2 x 2 x 3 x 263 x 701
Step 4: Therefore, the least common multiple of 8412 and 8416 is 17698848.