Least Common Multiple (LCM) of 69 and 136
The least common multiple (LCM) of 69 and 136 is 9384.
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 136?
First, calculate the GCD of 69 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 136 = 0 remainder 69 |
| 2 | 136 ÷ 69 = 1 remainder 67 |
| 3 | 69 ÷ 67 = 1 remainder 2 |
| 4 | 67 ÷ 2 = 33 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 63 | 945 |
| 112 and 121 | 13552 |
| 198 and 48 | 1584 |
| 153 and 143 | 21879 |
| 62 and 103 | 6386 |