Find the LCM and HCF of the following integers by the prime factorization method 17,23 and 29.
step by step solution
Answers
Answer:
Explanation:
Follow the steps mentioned below to find the LCM of the given integer.
Step 1: Write down the prime factorization of each integer.
Step 2: Write the prime factorization of each integer in exponential form and select the highest power of all the factors that occur in any of these numbers.
Step 3: Find the product of factors found in step 2.
Follow the steps mentioned below to find the HCF of the given integer.
Step 1: Write down the prime factorization of each integer.
Step 2: Write the common factors of each integer.
Step 3: Find the product of factors found in step 2.
(1)
Prime factorization of 12: 2 × 2 × 3 = 22 × 3
Prime factorization of 15: 3 × 5
Prime factorization of 21: 3 × 7
LCM of 12, 15, and 21 is given as:
LCM(12, 15, 21) = 22 × 3 × 5 × 7 = 4 × 3 × 5 × 7 = 420
HCF of 12, 15, and 21 is given as:
Common factors of the three numbers are: 3
HCF(12, 15, 21) = 3
(2)
Prime factorization of 17: 17
Prime factorization of 23: 23
Prime factorization of 29: 29
LCM of 17, 23, and 29 is given as:
LCM(17, 23, 29) = 17 × 23 × 29 = 11339
HCF of 17, 23, and 29 is given as:
Since there's not any common factor
Hence, HCF(17, 23, 29) = 1
(3)
Prime factorization of 8: 2 × 2 × 2 = 23
Prime factorization of 9: 3 × 3 = 32
Prime factorization of 25: 5 × 5 = 52
LCM of 8, 9, and 25 is given as:
LCM(8, 9, 25) = 23 × 32 × 52 = 8 × 9 × 25 =1800
HCF of 8, 9, and 25 is given as:
Since there's no common factor
Hence, HCF(8, 9, 25) = 1
Thus, (1) LCM(12, 15, 21) = 420, HCF(12, 15, 21) = 3 (2) LCM(17, 23, 29) = 11339, HCF(17, 23, 29) = 1 (3) LCM(8, 9, 25) = 1800, HCF(8, 9, 25) = 1.
Step-by-step explanation:
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Using prime factorisation method:
(i) 12, 15 and 21
Factor of 12=2×2×3
Factor of 15=3×5
Factor of 21=3×7
HCF (12,15,21)=3
LCM (12,15,21)=2×2×3×5×7=420
(ii) 17, 23 and 29
Factor of 17=1×17
Factor of 23=1×23
Factor of 29=1×29
HCF (17,23,29)=1
LCM (17,23,29)=1×17×23×29=11,339
(iii) 8, 9 and 25
Factor of 8=2×2×2×1
Factor of 9=3×3×1
Factor of 25=5×5×1
HCF (8,9,25)=1
LCM (8,9,25)=2×2×2×3×3×5×5=1,800