Least Common Multiple (LCM) of 72 and 97
The least common multiple (LCM) of 72 and 97 is 6984.
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 97?
First, calculate the GCD of 72 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 97 = 0 remainder 72 |
| 2 | 97 ÷ 72 = 1 remainder 25 |
| 3 | 72 ÷ 25 = 2 remainder 22 |
| 4 | 25 ÷ 22 = 1 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 165 | 20130 |
| 181 and 187 | 33847 |
| 116 and 20 | 580 |
| 173 and 147 | 25431 |
| 113 and 159 | 17967 |