Least Common Multiple (LCM) of 118 and 169
The least common multiple (LCM) of 118 and 169 is 19942.
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 118 and 169?
First, calculate the GCD of 118 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 169 = 0 remainder 118 |
| 2 | 169 ÷ 118 = 1 remainder 51 |
| 3 | 118 ÷ 51 = 2 remainder 16 |
| 4 | 51 ÷ 16 = 3 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 100 | 5700 |
| 110 and 112 | 6160 |
| 99 and 41 | 4059 |
| 185 and 18 | 3330 |
| 12 and 198 | 396 |