Least Common Multiple (LCM) of 97 and 162
The least common multiple (LCM) of 97 and 162 is 15714.
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 97 and 162?
First, calculate the GCD of 97 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 162 = 0 remainder 97 |
| 2 | 162 ÷ 97 = 1 remainder 65 |
| 3 | 97 ÷ 65 = 1 remainder 32 |
| 4 | 65 ÷ 32 = 2 remainder 1 |
| 5 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 172 | 15996 |
| 80 and 59 | 4720 |
| 128 and 131 | 16768 |
| 145 and 190 | 5510 |
| 13 and 135 | 1755 |