Least Common Multiple (LCM) of 34 and 62
The least common multiple (LCM) of 34 and 62 is 1054.
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 34 and 62?
First, calculate the GCD of 34 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 62 = 0 remainder 34 |
| 2 | 62 ÷ 34 = 1 remainder 28 |
| 3 | 34 ÷ 28 = 1 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 98 | 8722 |
| 158 and 152 | 12008 |
| 71 and 190 | 13490 |
| 108 and 163 | 17604 |
| 171 and 41 | 7011 |