Least Common Multiple (LCM) of 74 and 97
The least common multiple (LCM) of 74 and 97 is 7178.
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 74 and 97?
First, calculate the GCD of 74 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 97 = 0 remainder 74 |
| 2 | 97 ÷ 74 = 1 remainder 23 |
| 3 | 74 ÷ 23 = 3 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 124 | 8060 |
| 86 and 35 | 3010 |
| 157 and 132 | 20724 |
| 197 and 85 | 16745 |
| 180 and 153 | 3060 |