Least Common Multiple (LCM) of 174 and 101
The least common multiple (LCM) of 174 and 101 is 17574.
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 101?
First, calculate the GCD of 174 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 101 = 1 remainder 73 |
| 2 | 101 ÷ 73 = 1 remainder 28 |
| 3 | 73 ÷ 28 = 2 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 116 | 580 |
| 91 and 181 | 16471 |
| 77 and 31 | 2387 |
| 52 and 146 | 3796 |
| 167 and 138 | 23046 |