Least Common Multiple (LCM) of 174 and 91
The least common multiple (LCM) of 174 and 91 is 15834.
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 91?
First, calculate the GCD of 174 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 91 = 1 remainder 83 |
| 2 | 91 ÷ 83 = 1 remainder 8 |
| 3 | 83 ÷ 8 = 10 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 160 | 14880 |
| 190 and 37 | 7030 |
| 194 and 123 | 23862 |
| 45 and 44 | 1980 |
| 118 and 161 | 18998 |