Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 160 and 178 the smallest integer that is 14240 that is divisible by both numbers.
Least Common Multiple (LCM) of 160 and 178 is 14240.
LCM(160,178) = 14240
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 160 and 178. First we will calculate the prime factors of 160 and 178.
Prime Factorization of 160
2 | 160 |
2 | 80 |
2 | 40 |
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 160 are 2,5. Prime factorization of 160 in exponential form is:
160 = 25×51
Prime Factorization of 178
2 | 178 |
89 | 89 |
1 |
Prime factors of 178 are 2,89. Prime factorization of 178 in exponential form is:
178 = 21×891
Now multiplying the highest exponent prime factors to calculate the LCM of 160 and 178.
LCM(160,178) = 25×51×891
LCM(160,178) = 14240
Factors of 160
List of positive integer factors of 160 that divides 160 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
Factors of 178
List of positive integer factors of 178 that divides 178 without a remainder.
1, 2, 89, 178
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 160 and 178, than apply into the LCM equation.
GCF(160,178) = 2
LCM(160,178) = ( 160 × 178) / 2
LCM(160,178) = 28480 / 2
LCM(160,178) = 14240
(i) The LCM of 178 and 160 is associative
LCM of 160 and 178 = LCM of 178 and 160
1. What is the LCM of 160 and 178?
Answer: LCM of 160 and 178 is 14240.
2. What are the Factors of 160?
Answer: Factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. There are 12 integers that are factors of 160. The greatest factor of 160 is 160.
3. What are the Factors of 178?
Answer: Factors of 178 are 1, 2, 89, 178. There are 4 integers that are factors of 178. The greatest factor of 178 is 178.
4. How to Find the LCM of 160 and 178?
Answer:
Least Common Multiple of 160 and 178 = 14240
Step 1: Find the prime factorization of 160
160 = 2 x 2 x 2 x 2 x 2 x 5
Step 2: Find the prime factorization of 178
178 = 2 x 89
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14240 = 2 x 2 x 2 x 2 x 2 x 5 x 89
Step 4: Therefore, the least common multiple of 160 and 178 is 14240.