Least Common Multiple (LCM) of 109 and 174
The least common multiple (LCM) of 109 and 174 is 18966.
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 109 and 174?
First, calculate the GCD of 109 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 174 = 0 remainder 109 |
| 2 | 174 ÷ 109 = 1 remainder 65 |
| 3 | 109 ÷ 65 = 1 remainder 44 |
| 4 | 65 ÷ 44 = 1 remainder 21 |
| 5 | 44 ÷ 21 = 2 remainder 2 |
| 6 | 21 ÷ 2 = 10 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 138 | 15594 |
| 23 and 42 | 966 |
| 180 and 162 | 1620 |
| 170 and 28 | 2380 |
| 150 and 56 | 4200 |