Least Common Multiple (LCM) of 97 and 118
The least common multiple (LCM) of 97 and 118 is 11446.
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 118?
First, calculate the GCD of 97 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 118 = 0 remainder 97 |
| 2 | 118 ÷ 97 = 1 remainder 21 |
| 3 | 97 ÷ 21 = 4 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 97 | 11446 |
| 176 and 87 | 15312 |
| 159 and 64 | 10176 |
| 168 and 31 | 5208 |
| 128 and 56 | 896 |