Least Common Multiple (LCM) of 174 and 197
The least common multiple (LCM) of 174 and 197 is 34278.
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 174 and 197?
First, calculate the GCD of 174 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 197 = 0 remainder 174 |
| 2 | 197 ÷ 174 = 1 remainder 23 |
| 3 | 174 ÷ 23 = 7 remainder 13 |
| 4 | 23 ÷ 13 = 1 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 43 | 8600 |
| 36 and 181 | 6516 |
| 110 and 129 | 14190 |
| 88 and 57 | 5016 |
| 91 and 122 | 11102 |