Least Common Multiple (LCM) of 140 and 174
The least common multiple (LCM) of 140 and 174 is 12180.
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 140 and 174?
First, calculate the GCD of 140 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 174 = 0 remainder 140 |
| 2 | 174 ÷ 140 = 1 remainder 34 |
| 3 | 140 ÷ 34 = 4 remainder 4 |
| 4 | 34 ÷ 4 = 8 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 97 | 10282 |
| 113 and 145 | 16385 |
| 165 and 96 | 5280 |
| 176 and 135 | 23760 |
| 188 and 49 | 9212 |