Least Common Multiple of 174 and 175
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 174 and 175 the smallest integer that is 30450 that is divisible by both numbers.
Least Common Multiple (LCM) of 174 and 175 is 30450.
LCM(174,175) = 30450
LCM of 174 and 175
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 174 and 175 by Prime method
- Least Common Multiple of 174 and 175 with GCF Formula
LCM of 174 and 175 is 30450
Least common multiple can be found by multiplying the highest exponent prime factors of 174 and 175. First we will calculate the prime factors of 174 and 175.
Prime Factorization of 174
| 2 | 174 |
| 3 | 87 |
| 29 | 29 |
| 1 |
Prime factors of 174 are 2, 3,29. Prime factorization of 174 in exponential form is:
174 = 21×31×291
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
Now multiplying the highest exponent prime factors to calculate the LCM of 174 and 175.
LCM(174,175) = 21×31×52×71×291
LCM(174,175) = 30450
Factors of 174
List of positive integer factors of 174 that divides 174 without a remainder.
1, 2, 3, 6, 29, 58, 87, 174
Factors of 175
List of positive integer factors of 175 that divides 175 without a remainder.
1, 5, 7, 25, 35, 175
Least Common Multiple of 174 and 175 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 174 and 175, than apply into the LCM equation.
GCF(174,175) = 1
LCM(174,175) = ( 174 × 175) / 1
LCM(174,175) = 30450 / 1
LCM(174,175) = 30450
Properties of LCM 174 and 175
(i) The LCM of 175 and 174 is associative
LCM of 174 and 175 = LCM of 175 and 174
Related Least Common Multiples of 174
Related Least Common Multiples of 175
Frequently Asked Questions on LCM of 174 and 175
1. What is the LCM of 174 and 175?
Answer: LCM of 174 and 175 is 30450.
2. What are the Factors of 174?
Answer: Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174. There are 8 integers that are factors of 174. The greatest factor of 174 is 174.
3. 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.
4. How to Find the LCM of 174 and 175?
Answer:
Least Common Multiple of 174 and 175 = 30450
Step 1: Find the prime factorization of 174
174 = 2 x 3 x 29
Step 2: Find the prime factorization of 175
175 = 5 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 30450 = 2 x 3 x 5 x 5 x 7 x 29
Step 4: Therefore, the least common multiple of 174 and 175 is 30450.