Least Common Multiple (LCM) of 69 and 40
The least common multiple (LCM) of 69 and 40 is 2760.
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 40?
First, calculate the GCD of 69 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 40 = 1 remainder 29 |
| 2 | 40 ÷ 29 = 1 remainder 11 |
| 3 | 29 ÷ 11 = 2 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 194 | 12998 |
| 175 and 37 | 6475 |
| 172 and 29 | 4988 |
| 155 and 191 | 29605 |
| 157 and 73 | 11461 |