What is the LCM of $\sqrt[2]{169}$, $\sqrt[3]{27}$, $\sqrt[3]{64}$ and $\sqrt[2]{144}$ ?
Calculate Roots First
First, simplify each radical term:
- The square root of 169 is 13: $\sqrt[2]{169} = 13$
- The cube root of 27 is 3: $\sqrt[3]{27} = 3$
- The cube root of 64 is 4: $\sqrt[3]{64} = 4$
- The square root of 144 is 12: $\sqrt[2]{144} = 12$
Find LCM of Simplified Numbers
Now, find the Least Common Multiple (LCM) of the resulting integers: 13, 3, 4, and 12.
Use the prime factorization method for LCM:
- Prime factors of 13: 13
- Prime factors of 3: 3
- Prime factors of 4: $2 \times 2 = 2^2$
- Prime factors of 12: $2 \times 2 \times 3 = 2^2 \times 3$
Calculate the LCM Value
To find the LCM, take the highest power of each prime factor present in the numbers:
LCM = $13^1 \times 3^1 \times 2^2$
LCM = $13 \times 3 \times 4$
LCM = $13 \times 12$
LCM = 156
The LCM of the given radical terms is 156.
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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.
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?
The sum of two numbers is 1215 and their HCF is 81. How many such pairs of numbers can be formed?
The LCM of two numbers in 48. Their ratio is 2:3 What is the sum of the numbers?
