Least Common Multiple (LCM) of 144 and 196
The least common multiple (LCM) of 144 and 196 is 7056.
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 144 and 196?
First, calculate the GCD of 144 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 196 = 0 remainder 144 |
| 2 | 196 ÷ 144 = 1 remainder 52 |
| 3 | 144 ÷ 52 = 2 remainder 40 |
| 4 | 52 ÷ 40 = 1 remainder 12 |
| 5 | 40 ÷ 12 = 3 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 150 | 1650 |
| 136 and 10 | 680 |
| 195 and 108 | 7020 |
| 46 and 55 | 2530 |
| 102 and 49 | 4998 |