Least Common Multiple (LCM) of 69 and 118
The least common multiple (LCM) of 69 and 118 is 8142.
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 69 and 118?
First, calculate the GCD of 69 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 118 = 0 remainder 69 |
| 2 | 118 ÷ 69 = 1 remainder 49 |
| 3 | 69 ÷ 49 = 1 remainder 20 |
| 4 | 49 ÷ 20 = 2 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 106 | 5406 |
| 156 and 161 | 25116 |
| 79 and 172 | 13588 |
| 164 and 126 | 10332 |
| 159 and 47 | 7473 |