Least Common Multiple (LCM) of 74 and 105
The least common multiple (LCM) of 74 and 105 is 7770.
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 105?
First, calculate the GCD of 74 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 105 = 0 remainder 74 |
| 2 | 105 ÷ 74 = 1 remainder 31 |
| 3 | 74 ÷ 31 = 2 remainder 12 |
| 4 | 31 ÷ 12 = 2 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 21 | 294 |
| 61 and 99 | 6039 |
| 87 and 66 | 1914 |
| 162 and 56 | 4536 |
| 151 and 158 | 23858 |