Least Common Multiple (LCM) of 196 and 69
The least common multiple (LCM) of 196 and 69 is 13524.
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 196 and 69?
First, calculate the GCD of 196 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 69 = 2 remainder 58 |
| 2 | 69 ÷ 58 = 1 remainder 11 |
| 3 | 58 ÷ 11 = 5 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 10 | 640 |
| 144 and 164 | 5904 |
| 45 and 106 | 4770 |
| 25 and 92 | 2300 |
| 87 and 123 | 3567 |