Least Common Multiple (LCM) of 155 and 114
The least common multiple (LCM) of 155 and 114 is 17670.
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 114?
First, calculate the GCD of 155 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 114 = 1 remainder 41 |
| 2 | 114 ÷ 41 = 2 remainder 32 |
| 3 | 41 ÷ 32 = 1 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 137 | 3973 |
| 59 and 113 | 6667 |
| 10 and 143 | 1430 |
| 109 and 177 | 19293 |
| 53 and 162 | 8586 |