Least Common Multiple (LCM) of 69 and 113
The least common multiple (LCM) of 69 and 113 is 7797.
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 113?
First, calculate the GCD of 69 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 113 = 0 remainder 69 |
| 2 | 113 ÷ 69 = 1 remainder 44 |
| 3 | 69 ÷ 44 = 1 remainder 25 |
| 4 | 44 ÷ 25 = 1 remainder 19 |
| 5 | 25 ÷ 19 = 1 remainder 6 |
| 6 | 19 ÷ 6 = 3 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 181 | 24435 |
| 17 and 131 | 2227 |
| 51 and 58 | 2958 |
| 192 and 176 | 2112 |
| 114 and 19 | 114 |