Least Common Multiple (LCM) of 49 and 118
The least common multiple (LCM) of 49 and 118 is 5782.
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 49 and 118?
First, calculate the GCD of 49 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 118 = 0 remainder 49 |
| 2 | 118 ÷ 49 = 2 remainder 20 |
| 3 | 49 ÷ 20 = 2 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 113 | 15820 |
| 173 and 142 | 24566 |
| 61 and 194 | 11834 |
| 168 and 120 | 840 |
| 172 and 168 | 7224 |