Least Common Multiple (LCM) of 113 and 155
The least common multiple (LCM) of 113 and 155 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 113 and 155?
First, calculate the GCD of 113 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 155 = 0 remainder 113 |
| 2 | 155 ÷ 113 = 1 remainder 42 |
| 3 | 113 ÷ 42 = 2 remainder 29 |
| 4 | 42 ÷ 29 = 1 remainder 13 |
| 5 | 29 ÷ 13 = 2 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 29 | 290 |
| 140 and 87 | 12180 |
| 141 and 76 | 10716 |
| 114 and 21 | 798 |
| 171 and 104 | 17784 |