Least Common Multiple (LCM) of 67 and 74
The least common multiple (LCM) of 67 and 74 is 4958.
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 67 and 74?
First, calculate the GCD of 67 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 74 = 0 remainder 67 |
| 2 | 74 ÷ 67 = 1 remainder 7 |
| 3 | 67 ÷ 7 = 9 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 31 | 4278 |
| 55 and 148 | 8140 |
| 161 and 22 | 3542 |
| 36 and 90 | 180 |
| 98 and 89 | 8722 |