Least Common Multiple (LCM) of 69 and 196
The least common multiple (LCM) of 69 and 196 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 69 and 196?
First, calculate the GCD of 69 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 196 = 0 remainder 69 |
| 2 | 196 ÷ 69 = 2 remainder 58 |
| 3 | 69 ÷ 58 = 1 remainder 11 |
| 4 | 58 ÷ 11 = 5 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 162 | 2754 |
| 99 and 175 | 17325 |
| 182 and 131 | 23842 |
| 14 and 22 | 154 |
| 141 and 160 | 22560 |