Least Common Multiple (LCM) of 174 and 97
The least common multiple (LCM) of 174 and 97 is 16878.
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 97?
First, calculate the GCD of 174 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 97 = 1 remainder 77 |
| 2 | 97 ÷ 77 = 1 remainder 20 |
| 3 | 77 ÷ 20 = 3 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 92 | 5796 |
| 108 and 47 | 5076 |
| 157 and 109 | 17113 |
| 116 and 65 | 7540 |
| 36 and 84 | 252 |