Least Common Multiple (LCM) of 101 and 174
The least common multiple (LCM) of 101 and 174 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 101 and 174?
First, calculate the GCD of 101 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 174 = 0 remainder 101 |
| 2 | 174 ÷ 101 = 1 remainder 73 |
| 3 | 101 ÷ 73 = 1 remainder 28 |
| 4 | 73 ÷ 28 = 2 remainder 17 |
| 5 | 28 ÷ 17 = 1 remainder 11 |
| 6 | 17 ÷ 11 = 1 remainder 6 |
| 7 | 11 ÷ 6 = 1 remainder 5 |
| 8 | 6 ÷ 5 = 1 remainder 1 |
| 9 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 140 | 3220 |
| 80 and 159 | 12720 |
| 19 and 156 | 2964 |
| 105 and 57 | 1995 |
| 31 and 75 | 2325 |