Least Common Multiple (LCM) of 15 and 69
The least common multiple (LCM) of 15 and 69 is 345.
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 15 and 69?
First, calculate the GCD of 15 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 69 = 0 remainder 15 |
| 2 | 69 ÷ 15 = 4 remainder 9 |
| 3 | 15 ÷ 9 = 1 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 17 | 170 |
| 95 and 189 | 17955 |
| 32 and 10 | 160 |
| 161 and 41 | 6601 |
| 120 and 183 | 7320 |