Least Common Multiple (LCM) of 45 and 196
The least common multiple (LCM) of 45 and 196 is 8820.
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 45 and 196?
First, calculate the GCD of 45 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 196 = 0 remainder 45 |
| 2 | 196 ÷ 45 = 4 remainder 16 |
| 3 | 45 ÷ 16 = 2 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 162 | 15876 |
| 37 and 80 | 2960 |
| 189 and 147 | 1323 |
| 35 and 62 | 2170 |
| 18 and 128 | 1152 |