Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8172 and 8176 the smallest integer that is 16703568 that is divisible by both numbers.
Least Common Multiple (LCM) of 8172 and 8176 is 16703568.
LCM(8172,8176) = 16703568
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 8172 and 8176. First we will calculate the prime factors of 8172 and 8176.
Prime Factorization of 8172
2 | 8172 |
2 | 4086 |
3 | 2043 |
3 | 681 |
227 | 227 |
1 |
Prime factors of 8172 are 2, 3,227. Prime factorization of 8172 in exponential form is:
8172 = 22×32×2271
Prime Factorization of 8176
2 | 8176 |
2 | 4088 |
2 | 2044 |
2 | 1022 |
7 | 511 |
73 | 73 |
1 |
Prime factors of 8176 are 2, 7,73. Prime factorization of 8176 in exponential form is:
8176 = 24×71×731
Now multiplying the highest exponent prime factors to calculate the LCM of 8172 and 8176.
LCM(8172,8176) = 24×32×71×731×2271
LCM(8172,8176) = 16703568
Factors of 8172
List of positive integer factors of 8172 that divides 8172 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724, 4086, 8172
Factors of 8176
List of positive integer factors of 8176 that divides 8176 without a remainder.
1, 2, 4, 7, 8, 14, 16, 28, 56, 73, 112, 146, 292, 511, 584, 1022, 1168, 2044, 4088, 8176
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8172 and 8176, than apply into the LCM equation.
GCF(8172,8176) = 4
LCM(8172,8176) = ( 8172 × 8176) / 4
LCM(8172,8176) = 66814272 / 4
LCM(8172,8176) = 16703568
(i) The LCM of 8176 and 8172 is associative
LCM of 8172 and 8176 = LCM of 8176 and 8172
1. What is the LCM of 8172 and 8176?
Answer: LCM of 8172 and 8176 is 16703568.
2. What are the Factors of 8172?
Answer: Factors of 8172 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724, 4086, 8172. There are 18 integers that are factors of 8172. The greatest factor of 8172 is 8172.
3. What are the Factors of 8176?
Answer: Factors of 8176 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 73, 112, 146, 292, 511, 584, 1022, 1168, 2044, 4088, 8176. There are 20 integers that are factors of 8176. The greatest factor of 8176 is 8176.
4. How to Find the LCM of 8172 and 8176?
Answer:
Least Common Multiple of 8172 and 8176 = 16703568
Step 1: Find the prime factorization of 8172
8172 = 2 x 2 x 3 x 3 x 227
Step 2: Find the prime factorization of 8176
8176 = 2 x 2 x 2 x 2 x 7 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 16703568 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 73 x 227
Step 4: Therefore, the least common multiple of 8172 and 8176 is 16703568.