Least Common Multiple (LCM) of 117 and 155
The least common multiple (LCM) of 117 and 155 is 18135.
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 117 and 155?
First, calculate the GCD of 117 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 155 = 0 remainder 117 |
| 2 | 155 ÷ 117 = 1 remainder 38 |
| 3 | 117 ÷ 38 = 3 remainder 3 |
| 4 | 38 ÷ 3 = 12 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 105 | 1155 |
| 167 and 143 | 23881 |
| 80 and 154 | 6160 |
| 170 and 80 | 1360 |
| 19 and 75 | 1425 |