Least Common Multiple (LCM) of 97 and 176
The least common multiple (LCM) of 97 and 176 is 17072.
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 176?
First, calculate the GCD of 97 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 176 = 0 remainder 97 |
| 2 | 176 ÷ 97 = 1 remainder 79 |
| 3 | 97 ÷ 79 = 1 remainder 18 |
| 4 | 79 ÷ 18 = 4 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 141 | 16356 |
| 130 and 109 | 14170 |
| 64 and 58 | 1856 |
| 121 and 176 | 1936 |
| 140 and 15 | 420 |