Finding LCM of 8, 12, and 20
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by each of the given numbers.
Prime Factorization Method
We can find the LCM using the prime factorization method:
- Step 1: Find the prime factorization of each number.
- $8 = 2 \times 2 \times 2 = 2^3$
- $12 = 2 \times 2 \times 3 = 2^2 \times 3^1$
- $20 = 2 \times 2 \times 5 = 2^2 \times 5^1$
- Step 2: Identify all the unique prime factors present in any of the factorizations.
The unique prime factors are 2, 3, and 5.
- Step 3: Take the highest power of each unique prime factor.
- Highest power of 2 is $2^3$.
- Highest power of 3 is $3^1$.
- Highest power of 5 is $5^1$.
- Step 4: Multiply these highest powers together to get the LCM.
LCM = $2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 120$.
Therefore, the LCM of 8, 12, and 20 is 120.
Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
