Divide the LCM of 20,30 and40 by their HCF
To find the LCM (Least Common Multiple) of 20, 30, and 40, we need to find the smallest number that is divisible by all three numbers.
Prime factorization of 20: 2^2 * 5
Prime factorization of 30: 2 * 3 * 5
Prime factorization of 40: 2^3 * 5
The LCM is found by taking the highest powers of all prime factors that appear in the prime factorizations of the numbers.
So, LCM of 20, 30, and 40 = 2^3 * 3 * 5 = 120
Now, let's find the HCF (Highest Common Factor) of 20, 30, and 40. It is the largest number that divides all three numbers.
The common prime factors of 20, 30, and 40 are 2 and 5.
So, HCF of 20, 30, and 40 = 2 * 5 = 10
Dividing the LCM by the HCF:
120 รท 10 = 12
Therefore, the LCM of 20, 30, and 40 divided by their HCF is 12.
To find the answer, we need to calculate the LCM (Least Common Multiple) and HCF (Highest Common Factor) of 20, 30, and 40.
Step 1: Find the LCM
To calculate the LCM, we will find the prime factorization of each number and multiply the highest power of each prime factor.
Prime factorization of 20: 2^2 * 5^1
Prime factorization of 30: 2^1 * 3^1 * 5^1
Prime factorization of 40: 2^3 * 5^1
Multiply the highest power of each prime factor:
LCM = 2^3 * 3^1 * 5^1
LCM = 2 * 2 * 2 * 3 * 5
LCM = 120
Step 2: Find the HCF
To calculate the HCF, we need to find the highest power of each common prime factor.
Highest power of 2: 2^2
Highest power of 3: 3^0
Highest power of 5: 5^1
HCF = 2^2 * 3^0 * 5^1
HCF = 2^2 * 1 * 5
HCF = 20
Step 3: Divide LCM by HCF
Divide the LCM by the HCF to get the final result:
120 / 20 = 6
Therefore, the result of dividing the LCM of 20, 30, and 40 by their HCF is 6.