Least Common Multiple (LCM) of 169 and 196
The least common multiple (LCM) of 169 and 196 is 33124.
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 169 and 196?
First, calculate the GCD of 169 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 196 = 0 remainder 169 |
| 2 | 196 ÷ 169 = 1 remainder 27 |
| 3 | 169 ÷ 27 = 6 remainder 7 |
| 4 | 27 ÷ 7 = 3 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 100 | 2700 |
| 82 and 197 | 16154 |
| 123 and 194 | 23862 |
| 99 and 137 | 13563 |
| 162 and 56 | 4536 |