Least Common Multiple (LCM) of 118 and 168
The least common multiple (LCM) of 118 and 168 is 9912.
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 168?
First, calculate the GCD of 118 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 168 = 0 remainder 118 |
| 2 | 168 ÷ 118 = 1 remainder 50 |
| 3 | 118 ÷ 50 = 2 remainder 18 |
| 4 | 50 ÷ 18 = 2 remainder 14 |
| 5 | 18 ÷ 14 = 1 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 163 | 16952 |
| 173 and 160 | 27680 |
| 34 and 35 | 1190 |
| 128 and 150 | 9600 |
| 136 and 180 | 6120 |