Least Common Multiple (LCM) of 72 and 196
The least common multiple (LCM) of 72 and 196 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 72 and 196?
First, calculate the GCD of 72 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 196 = 0 remainder 72 |
| 2 | 196 ÷ 72 = 2 remainder 52 |
| 3 | 72 ÷ 52 = 1 remainder 20 |
| 4 | 52 ÷ 20 = 2 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 39 | 1404 |
| 40 and 171 | 6840 |
| 59 and 82 | 4838 |
| 115 and 178 | 20470 |
| 28 and 21 | 84 |