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SubjectsMathematics
अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य
In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.
TOPIC PRACTICE
Up to 20 questions from this page. Select your focus, then start.
Step 1: For two numbers, a special relation is used. Step 2: The product of HCF and LCM equals the product of the two numbers. Step 3: Apply this relation directly only for two numbers.
View question detailsStep 1: (22=2\times11) and (33=3\times11). Step 2: The common prime factor is (11). Step 3: Therefore, the HCF is (11).
View question detailsStep 1: (22=2\times11) and (33=3\times11). Step 2: For LCM, include (2), (3), and (11). Step 3: (2\times3\times11=66), so the answer is (66).
View question detailsStep 1: (30=2\times3\times5) and (42=2\times3\times7). Step 2: The common prime factors are (2) and (3). Step 3: (2\times3=6), so the HCF is (6).
View question detailsStep 1: (30=2\times3\times5) and (42=2\times3\times7). Step 2: Take (2), (3), (5), and (7) with highest powers. Step 3: (2\times3\times5\times7=210), so the LCM is (210).
View question detailsStep 1: (56=2^3\times7) and (84=2^2\times3\times7). Step 2: The smaller powers of common factors are (2^2) and (7). Step 3: (4\times7=28), so the HCF is (28).
View question detailsStep 1: (56=2^3\times7) and (84=2^2\times3\times7). Step 2: The highest powers are (2^3), (3), and (7). Step 3: (8\times3\times7=168), so the answer is (168).
View question detailsStep 1: (81=3^4) and (108=2^2\times3^3). Step 2: The common prime factor is (3), and the smaller power is (3^3). Step 3: (3^3=27), so the HCF is (27).
View question detailsStep 1: (81=3^4) and (108=2^2\times3^3). Step 2: For LCM, take (2^2) and (3^4). Step 3: (4\times81=324), so the LCM is (324).
View question detailsStep 1: (45=3^2\times5) and (90=2\times3^2\times5). Step 2: All prime factors of (45) are present in (90). Step 3: Therefore, the HCF is (45).
View question detailsStep 1: (45=3^2\times5) and (90=2\times3^2\times5). Step 2: The number (90) already contains all factors of (45). Step 3: So the LCM is (90).
View question detailsStep 1: (24=2^3\times3), (36=2^2\times3^2), and (48=2^4\times3). Step 2: The common smaller powers are (2^2) and (3). Step 3: (4\times3=12), so the HCF is (12).
View question detailsStep 1: (24=2^3\times3), (36=2^2\times3^2), and (48=2^4\times3). Step 2: The highest powers are (2^4) and (3^2). Step 3: (16\times9=144), so the LCM is (144).
View question detailsStep 1: (20=2^2\times5), (50=2\times5^2), and (70=2\times5\times7). Step 2: The common factors in all three are (2) and (5). Step 3: (2\times5=10), so the HCF is (10).
View question detailsStep 1: (20=2^2\times5), (50=2\times5^2), and (70=2\times5\times7). Step 2: The highest powers are (2^2), (5^2), and (7). Step 3: (4\times25\times7=700), so the answer is (700).
View question detailsStep 1: (42=2\times3\times7), (63=3^2\times7), and (105=3\times5\times7). Step 2: The common prime factors are (3) and (7). Step 3: (3\times7=21), so the answer is (21).
View question detailsStep 1: (42=2\times3\times7), (63=3^2\times7), and (105=3\times5\times7). Step 2: The highest powers are (2), (3^2), (5), and (7). Step 3: (2\times9\times5\times7=630), so the LCM is (630).
View question detailsStep 1: The common prime factors are (2), (3), and (5). Step 2: The smaller powers are (2^2), (3), and (5). Step 3: (4\times3\times5=60), so the HCF is (60).
View question detailsStep 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^3), (3^2), and (5). Step 3: (8\times9\times5=360), so the answer is (360).
View question detailsStep 1: The common factors are (2) and (3). Step 2: The smaller powers are (2^3) and (3). Step 3: (2^3\times3=24), so the HCF is (24).
View question detailsQUIZ COMPLETE
