Least Common Multiple (LCM) of 174 and 110
The least common multiple (LCM) of 174 and 110 is 9570.
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 110?
First, calculate the GCD of 174 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 110 = 1 remainder 64 |
| 2 | 110 ÷ 64 = 1 remainder 46 |
| 3 | 64 ÷ 46 = 1 remainder 18 |
| 4 | 46 ÷ 18 = 2 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 167 | 1670 |
| 137 and 79 | 10823 |
| 155 and 114 | 17670 |
| 58 and 23 | 1334 |
| 136 and 20 | 680 |