Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 145 and 146 the smallest integer that is 21170 that is divisible by both numbers.
Least Common Multiple (LCM) of 145 and 146 is 21170.
LCM(145,146) = 21170
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 145 and 146. First we will calculate the prime factors of 145 and 146.
Prime Factorization of 145
5 | 145 |
29 | 29 |
1 |
Prime factors of 145 are 5,29. Prime factorization of 145 in exponential form is:
145 = 51×291
Prime Factorization of 146
2 | 146 |
73 | 73 |
1 |
Prime factors of 146 are 2,73. Prime factorization of 146 in exponential form is:
146 = 21×731
Now multiplying the highest exponent prime factors to calculate the LCM of 145 and 146.
LCM(145,146) = 21×51×291×731
LCM(145,146) = 21170
Factors of 145
List of positive integer factors of 145 that divides 145 without a remainder.
1, 5, 29, 145
Factors of 146
List of positive integer factors of 146 that divides 146 without a remainder.
1, 2, 73, 146
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 145 and 146, than apply into the LCM equation.
GCF(145,146) = 1
LCM(145,146) = ( 145 × 146) / 1
LCM(145,146) = 21170 / 1
LCM(145,146) = 21170
(i) The LCM of 146 and 145 is associative
LCM of 145 and 146 = LCM of 146 and 145
1. What is the LCM of 145 and 146?
Answer: LCM of 145 and 146 is 21170.
2. What are the Factors of 145?
Answer: Factors of 145 are 1, 5, 29, 145. There are 4 integers that are factors of 145. The greatest factor of 145 is 145.
3. What are the Factors of 146?
Answer: Factors of 146 are 1, 2, 73, 146. There are 4 integers that are factors of 146. The greatest factor of 146 is 146.
4. How to Find the LCM of 145 and 146?
Answer:
Least Common Multiple of 145 and 146 = 21170
Step 1: Find the prime factorization of 145
145 = 5 x 29
Step 2: Find the prime factorization of 146
146 = 2 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 = 21170 = 2 x 5 x 29 x 73
Step 4: Therefore, the least common multiple of 145 and 146 is 21170.