To find the difference between the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 184 and 345, follow these steps:
Calculate HCF of 184 and 345
We can use the Euclidean algorithm or prime factorization to find the HCF.
- Prime Factorization Method:
- Factorize 184: \(184 = 2 \times 92 = 2 \times 2 \times 46 = 2 \times 2 \times 2 \times 23 = 2^3 \times 23^1\)
- Factorize 345: \(345 = 3 \times 115 = 3 \times 5 \times 23 = 3^1 \times 5^1 \times 23^1\)
- The common prime factor is 23.
- Therefore, HCF(184, 345) = 23.
Calculate LCM of 184 and 345
Use the relationship between HCF and LCM:
LCM(a, b) = \(\frac{(a \times b)}{\text{HCF}(a, b)}\)
Substitute the values:
LCM(184, 345) = \(\frac{(184 \times 345)}{23}\)
Calculate the LCM:
LCM(184, 345) = \(184 \times \frac{345}{23}\)
LCM(184, 345) = \(184 \times 15\)
LCM(184, 345) = 2760
Find the Difference
Subtract the HCF from the LCM:
Difference = LCM - HCF
Difference = \(2760 - 23\)
Difference = 2737
The difference between the HCF and LCM of 184 and 345 is 2737.
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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.
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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?
