Least Common Multiple (LCM) of 97 and 149
The least common multiple (LCM) of 97 and 149 is 14453.
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 149?
First, calculate the GCD of 97 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 149 = 0 remainder 97 |
| 2 | 149 ÷ 97 = 1 remainder 52 |
| 3 | 97 ÷ 52 = 1 remainder 45 |
| 4 | 52 ÷ 45 = 1 remainder 7 |
| 5 | 45 ÷ 7 = 6 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 192 | 19776 |
| 174 and 28 | 2436 |
| 108 and 171 | 2052 |
| 180 and 164 | 7380 |
| 72 and 29 | 2088 |