Least Common Multiple (LCM) of 72 and 197
The least common multiple (LCM) of 72 and 197 is 14184.
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 197?
First, calculate the GCD of 72 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 197 = 0 remainder 72 |
| 2 | 197 ÷ 72 = 2 remainder 53 |
| 3 | 72 ÷ 53 = 1 remainder 19 |
| 4 | 53 ÷ 19 = 2 remainder 15 |
| 5 | 19 ÷ 15 = 1 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 186 | 32550 |
| 180 and 59 | 10620 |
| 98 and 39 | 3822 |
| 149 and 196 | 29204 |
| 111 and 134 | 14874 |