Least Common Multiple (LCM) of 36 and 69
The least common multiple (LCM) of 36 and 69 is 828.
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 36 and 69?
First, calculate the GCD of 36 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 69 = 0 remainder 36 |
| 2 | 69 ÷ 36 = 1 remainder 33 |
| 3 | 36 ÷ 33 = 1 remainder 3 |
| 4 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 78 | 3900 |
| 107 and 120 | 12840 |
| 107 and 141 | 15087 |
| 112 and 61 | 6832 |
| 35 and 11 | 385 |