Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 175 and 182 the smallest integer that is 4550 that is divisible by both numbers.
Least Common Multiple (LCM) of 175 and 182 is 4550.
LCM(175,182) = 4550
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 175 and 182. First we will calculate the prime factors of 175 and 182.
Prime Factorization of 175
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 175 are 5,7. Prime factorization of 175 in exponential form is:
175 = 52×71
Prime Factorization of 182
2 | 182 |
7 | 91 |
13 | 13 |
1 |
Prime factors of 182 are 2, 7,13. Prime factorization of 182 in exponential form is:
182 = 21×71×131
Now multiplying the highest exponent prime factors to calculate the LCM of 175 and 182.
LCM(175,182) = 21×52×71×131
LCM(175,182) = 4550
Factors of 175
List of positive integer factors of 175 that divides 175 without a remainder.
1, 5, 7, 25, 35, 175
Factors of 182
List of positive integer factors of 182 that divides 182 without a remainder.
1, 2, 7, 13, 14, 26, 91, 182
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 175 and 182, than apply into the LCM equation.
GCF(175,182) = 7
LCM(175,182) = ( 175 × 182) / 7
LCM(175,182) = 31850 / 7
LCM(175,182) = 4550
(i) The LCM of 182 and 175 is associative
LCM of 175 and 182 = LCM of 182 and 175
1. What is the LCM of 175 and 182?
Answer: LCM of 175 and 182 is 4550.
2. What are the Factors of 175?
Answer: Factors of 175 are 1, 5, 7, 25, 35, 175. There are 6 integers that are factors of 175. The greatest factor of 175 is 175.
3. What are the Factors of 182?
Answer: Factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182. There are 8 integers that are factors of 182. The greatest factor of 182 is 182.
4. How to Find the LCM of 175 and 182?
Answer:
Least Common Multiple of 175 and 182 = 4550
Step 1: Find the prime factorization of 175
175 = 5 x 5 x 7
Step 2: Find the prime factorization of 182
182 = 2 x 7 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 = 4550 = 2 x 5 x 5 x 7 x 13
Step 4: Therefore, the least common multiple of 175 and 182 is 4550.