Least Common Multiple (LCM) of 118 and 159
The least common multiple (LCM) of 118 and 159 is 18762.
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 159?
First, calculate the GCD of 118 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 159 = 0 remainder 118 |
| 2 | 159 ÷ 118 = 1 remainder 41 |
| 3 | 118 ÷ 41 = 2 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 |
|---|---|
| 113 and 131 | 14803 |
| 21 and 147 | 147 |
| 174 and 60 | 1740 |
| 135 and 113 | 15255 |
| 10 and 137 | 1370 |