Least Common Multiple (LCM) of 63 and 119
The least common multiple (LCM) of 63 and 119 is 1071.
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 63 and 119?
First, calculate the GCD of 63 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 119 = 0 remainder 63 |
| 2 | 119 ÷ 63 = 1 remainder 56 |
| 3 | 63 ÷ 56 = 1 remainder 7 |
| 4 | 56 ÷ 7 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 145 | 24215 |
| 98 and 66 | 3234 |
| 100 and 173 | 17300 |
| 148 and 133 | 19684 |
| 65 and 128 | 8320 |