Least Common Multiple (LCM) of 155 and 113
The least common multiple (LCM) of 155 and 113 is 17515.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 155 and 113?
First, calculate the GCD of 155 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 113 = 1 remainder 42 |
| 2 | 113 ÷ 42 = 2 remainder 29 |
| 3 | 42 ÷ 29 = 1 remainder 13 |
| 4 | 29 ÷ 13 = 2 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 139 | 19182 |
| 179 and 105 | 18795 |
| 177 and 134 | 23718 |
| 77 and 141 | 10857 |
| 72 and 42 | 504 |