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 |
|---|---|
| 48 and 178 | 4272 |
| 159 and 50 | 7950 |
| 109 and 67 | 7303 |
| 128 and 143 | 18304 |
| 155 and 24 | 3720 |