Least Common Multiple (LCM) of 67 and 151
The least common multiple (LCM) of 67 and 151 is 10117.
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 151?
First, calculate the GCD of 67 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 151 = 0 remainder 67 |
| 2 | 151 ÷ 67 = 2 remainder 17 |
| 3 | 67 ÷ 17 = 3 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 90 | 4770 |
| 149 and 171 | 25479 |
| 112 and 193 | 21616 |
| 88 and 110 | 440 |
| 22 and 178 | 1958 |