Question1: find the least perfect squared number that is divisible by 12, 16,20 and 24
Question1: find the least perfect squared number that is divisible by 12, 16,20 and 24.
Plz change the method of this question this method
I cannot Understand the first solving method of this question
Can you please change the method of this question.
To find the least perfect squared number that is divisible by 12, 16, 20, and 24, we need to find the least common multiple (LCM) of these numbers first.
Step 1: Prime factorize the given numbers.
12 = 2^2 * 3
16 = 2^4
20 = 2^2 * 5
24 = 2^3 * 3
Step 2: Identify the highest exponent for each prime factor.
The highest exponents are 2 for 2 and 1 for 3 and 5.
Step 3: Multiply the prime factors with the highest exponents.
2^2 * 3^1 * 5^1 = 4 * 3 * 5 = 60
Step 4: Determine the least perfect square greater than or equal to the LCM obtained.
The least perfect square greater than or equal to 60 is 7^2 = 49.
Hence, the least perfect squared number that is divisible by 12, 16, 20, and 24 is 49.
3600
1440 is not perfect square
12 = 4*3
16 = 4*4
20 = 4*5
24 = 4*6 = 4*2*3
perfect squares come in pairs of equal factors
so we need 4*4*25*9 = 3600
12 = 4*3
16 = 4*4
20 = 4*5
24 = 4*6 = 4*2*3
perfect squares come in pairs of equal factors
so we need 4*4*25*9 = 3600
is the right method and 3600 is the right answer.but it is little bit tricky.
NOTE:perfect squares come in pairs of equal factors
we have four (4) so there are two (4)in the last step.
we have two (3) so there are only one(3)in the last step.
we already have 5 so we need an extra 5 to make perfect square.
12=4*3
16=4*2*2
20=4*5
24=4*3*2
Highest common factor =4*2*3=24
Least perfect square number =24*5*2 =24^2*5^2*2^2
=376*25*4 =376*100
Answer is =37600
This answer is totally wrong
my answer is 1440
12=4*3
16=4*2*2
20=4*5
24=4*3*2
Highest common factor =4*2*3=24
Least perfect square number =24*5*2 =24^2*5^2*2^2
=376*25*4 =376*100
Answer is =37600