Least Common Multiple (LCM) of 67 and 153
The least common multiple (LCM) of 67 and 153 is 10251.
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 153?
First, calculate the GCD of 67 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 153 = 0 remainder 67 |
| 2 | 153 ÷ 67 = 2 remainder 19 |
| 3 | 67 ÷ 19 = 3 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 52 | 1040 |
| 178 and 135 | 24030 |
| 57 and 104 | 5928 |
| 117 and 141 | 5499 |
| 55 and 87 | 4785 |