Least Common Multiple (LCM) of 196 and 72
The least common multiple (LCM) of 196 and 72 is 3528.
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 196 and 72?
First, calculate the GCD of 196 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 72 = 2 remainder 52 |
| 2 | 72 ÷ 52 = 1 remainder 20 |
| 3 | 52 ÷ 20 = 2 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 138 | 5382 |
| 157 and 152 | 23864 |
| 90 and 43 | 3870 |
| 71 and 142 | 142 |
| 105 and 23 | 2415 |