Least Common Multiple (LCM) of 195 and 118
The least common multiple (LCM) of 195 and 118 is 23010.
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 195 and 118?
First, calculate the GCD of 195 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 118 = 1 remainder 77 |
| 2 | 118 ÷ 77 = 1 remainder 41 |
| 3 | 77 ÷ 41 = 1 remainder 36 |
| 4 | 41 ÷ 36 = 1 remainder 5 |
| 5 | 36 ÷ 5 = 7 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 51 | 9129 |
| 23 and 176 | 4048 |
| 33 and 102 | 1122 |
| 68 and 15 | 1020 |
| 38 and 55 | 2090 |