Least Common Multiple (LCM) of 118 and 139
The least common multiple (LCM) of 118 and 139 is 16402.
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 139?
First, calculate the GCD of 118 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 139 = 0 remainder 118 |
| 2 | 139 ÷ 118 = 1 remainder 21 |
| 3 | 118 ÷ 21 = 5 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 157 | 25905 |
| 52 and 44 | 572 |
| 40 and 163 | 6520 |
| 15 and 68 | 1020 |
| 27 and 111 | 999 |