Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 172 and 176 the smallest integer that is 7568 that is divisible by both numbers.
Least Common Multiple (LCM) of 172 and 176 is 7568.
LCM(172,176) = 7568
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 172 and 176. First we will calculate the prime factors of 172 and 176.
Prime Factorization of 172
2 | 172 |
2 | 86 |
43 | 43 |
1 |
Prime factors of 172 are 2,43. Prime factorization of 172 in exponential form is:
172 = 22×431
Prime Factorization of 176
2 | 176 |
2 | 88 |
2 | 44 |
2 | 22 |
11 | 11 |
1 |
Prime factors of 176 are 2,11. Prime factorization of 176 in exponential form is:
176 = 24×111
Now multiplying the highest exponent prime factors to calculate the LCM of 172 and 176.
LCM(172,176) = 24×111×431
LCM(172,176) = 7568
Factors of 172
List of positive integer factors of 172 that divides 172 without a remainder.
1, 2, 4, 43, 86, 172
Factors of 176
List of positive integer factors of 176 that divides 176 without a remainder.
1, 2, 4, 8, 11, 16, 22, 44, 88, 176
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 172 and 176, than apply into the LCM equation.
GCF(172,176) = 4
LCM(172,176) = ( 172 × 176) / 4
LCM(172,176) = 30272 / 4
LCM(172,176) = 7568
(i) The LCM of 176 and 172 is associative
LCM of 172 and 176 = LCM of 176 and 172
1. What is the LCM of 172 and 176?
Answer: LCM of 172 and 176 is 7568.
2. What are the Factors of 172?
Answer: Factors of 172 are 1, 2, 4, 43, 86, 172. There are 6 integers that are factors of 172. The greatest factor of 172 is 172.
3. What are the Factors of 176?
Answer: Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. There are 10 integers that are factors of 176. The greatest factor of 176 is 176.
4. How to Find the LCM of 172 and 176?
Answer:
Least Common Multiple of 172 and 176 = 7568
Step 1: Find the prime factorization of 172
172 = 2 x 2 x 43
Step 2: Find the prime factorization of 176
176 = 2 x 2 x 2 x 2 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7568 = 2 x 2 x 2 x 2 x 11 x 43
Step 4: Therefore, the least common multiple of 172 and 176 is 7568.