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 |
|---|---|
| 37 and 82 | 3034 |
| 132 and 41 | 5412 |
| 153 and 91 | 13923 |
| 168 and 146 | 12264 |
| 180 and 128 | 5760 |