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What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times?
Most Upvoted Answer
What is the smallest number which when divided by 24, 36 and 54 given ...
24=2×2×2×3
36=2×2×3×3
54=2×3×3×3
LCM of above numbers=2×2×2×3×3×3=216
Add=216+5=221.
36=2×2×3×3
54=2×3×3×3
LCM of above numbers=2×2×2×3×3×3=216
Add=216+5=221.
Community Answer
What is the smallest number which when divided by 24, 36 and 54 given ...
Smallest Number with a Remainder of 5
To find the smallest number that gives a remainder of 5 when divided by 24, 36, and 54, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest number that is divisible by all the given numbers.
Finding the LCM
To find the LCM, we can use the prime factorization method. We break down each number into its prime factors and then take the highest power of each prime factor.
Prime Factorization of 24
24 can be written as 2 x 2 x 2 x 3 or 2^3 x 3
Prime Factorization of 36
36 can be written as 2 x 2 x 3 x 3 or 2^2 x 3^2
Prime Factorization of 54
54 can be written as 2 x 3 x 3 x 3 or 2 x 3^3
Finding the LCM
To find the LCM, we take the highest power of each prime factor:
2^3 x 3^3 = 8 x 27 = 216
Therefore, the LCM of 24, 36, and 54 is 216.
Finding the Smallest Number
To find the smallest number that gives a remainder of 5 when divided by 24, 36, and 54, we need to find the smallest multiple of 216 that leaves a remainder of 5.
We can start by adding 5 to the LCM:
216 + 5 = 221
However, 221 is not divisible by 24, 36, or 54, so we need to find the next multiple of 216 that leaves a remainder of 5.
We can continue adding multiples of 216 until we find a number that satisfies the condition:
216 x 2 + 5 = 437
437 is not divisible by 24, 36, or 54, so we continue:
216 x 3 + 5 = 653
653 is not divisible by 24, 36, or 54, so we continue:
216 x 4 + 5 = 869
869 is not divisible by 24, 36, or 54, so we continue:
216 x 5 + 5 = 1085
1085 is not divisible by 24, 36, or 54, so we continue:
216 x 6 + 5 = 1301
1301 is not divisible by 24, 36, or 54, so we continue:
216 x 7 + 5 = 1517
1517 is not divisible by 24, 36, or 54, so we continue:
216 x 8 + 5 = 1733
1733 is not divisible by 24, 36, or 54, so we continue:
216 x 9 + 5 = 1949
1949 is not divisible by 24, 36, or 54, so we continue:
216 x 10 + 5 = 2165
2165 is not divisible by 24, 36, or 54, so we continue:
216
To find the smallest number that gives a remainder of 5 when divided by 24, 36, and 54, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest number that is divisible by all the given numbers.
Finding the LCM
To find the LCM, we can use the prime factorization method. We break down each number into its prime factors and then take the highest power of each prime factor.
Prime Factorization of 24
24 can be written as 2 x 2 x 2 x 3 or 2^3 x 3
Prime Factorization of 36
36 can be written as 2 x 2 x 3 x 3 or 2^2 x 3^2
Prime Factorization of 54
54 can be written as 2 x 3 x 3 x 3 or 2 x 3^3
Finding the LCM
To find the LCM, we take the highest power of each prime factor:
2^3 x 3^3 = 8 x 27 = 216
Therefore, the LCM of 24, 36, and 54 is 216.
Finding the Smallest Number
To find the smallest number that gives a remainder of 5 when divided by 24, 36, and 54, we need to find the smallest multiple of 216 that leaves a remainder of 5.
We can start by adding 5 to the LCM:
216 + 5 = 221
However, 221 is not divisible by 24, 36, or 54, so we need to find the next multiple of 216 that leaves a remainder of 5.
We can continue adding multiples of 216 until we find a number that satisfies the condition:
216 x 2 + 5 = 437
437 is not divisible by 24, 36, or 54, so we continue:
216 x 3 + 5 = 653
653 is not divisible by 24, 36, or 54, so we continue:
216 x 4 + 5 = 869
869 is not divisible by 24, 36, or 54, so we continue:
216 x 5 + 5 = 1085
1085 is not divisible by 24, 36, or 54, so we continue:
216 x 6 + 5 = 1301
1301 is not divisible by 24, 36, or 54, so we continue:
216 x 7 + 5 = 1517
1517 is not divisible by 24, 36, or 54, so we continue:
216 x 8 + 5 = 1733
1733 is not divisible by 24, 36, or 54, so we continue:
216 x 9 + 5 = 1949
1949 is not divisible by 24, 36, or 54, so we continue:
216 x 10 + 5 = 2165
2165 is not divisible by 24, 36, or 54, so we continue:
216
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What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times?
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What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times?.
What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest number which when divided by 24, 36 and 54 given a reminder of 5 each times?.
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