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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.
For two positive integers, the relation is: product = HCF \(\times\) LCM. Therefore, HCF \(=3780\div315=12\). Hence, option B is correct. Exam tip: To find the HCF, divide the product by the LCM and verify that the quotient is a whole number.
View question detailsStep 1: (18=2\times3^2) and (24=2^3\times3). Step 2: Taking the smaller powers of common prime factors gives (2\times3=6). Step 3: For HCF, take only common prime factors.
View question detailsStep 1: (18=2\times3^2) and (24=2^3\times3). Step 2: Taking the highest powers of all prime factors gives (2^3\times3^2=72). Step 3: For LCM, include both common and uncommon prime factors.
View question detailsStep 1: (40=2^3\times5) and (60=2^2\times3\times5). Step 2: The common factors with smaller powers are (2^2) and (5). Step 3: (2^2\times5=20), so the HCF is (20).
View question detailsStep 1: (40=2^3\times5) and (60=2^2\times3\times5). Step 2: Use the highest powers (2^3), (3), and (5). Step 3: (2^3\times3\times5=120), so the LCM is (120).
View question detailsStep 1: (45=3^2\times5) and (75=3\times5^2). Step 2: Take the smaller powers of the common prime factors (3) and (5). Step 3: (3\times5=15), so the HCF is (15).
View question detailsStep 1: (45=3^2\times5) and (75=3\times5^2). Step 2: Take the highest powers (3^2) and (5^2). Step 3: (3^2\times5^2=225), so the LCM is (225).
View question detailsStep 1: (32=2^5) and (48=2^4\times3). Step 2: The only common prime factor is (2), and the smaller power is (2^4). Step 3: (2^4=16), so the HCF is (16).
View question detailsStep 1: (32=2^5) and (48=2^4\times3). Step 2: Take the highest powers (2^5) and (3). Step 3: (2^5\times3=96), so the LCM is (96).
View question detailsStep 1: (27=3^3) and (36=2^2\times3^2). Step 2: The common prime factor is (3), and the smaller power is (3^2). Step 3: (3^2=9), so the HCF is (9).
View question detailsStep 1: (27=3^3) and (36=2^2\times3^2). Step 2: For LCM, take the highest powers (2^2) and (3^3). Step 3: (2^2\times3^3=108), so the LCM is (108).
View question detailsStep 1: (72=2^3\times3^2) and (90=2\times3^2\times5). Step 2: The smaller powers of common factors are (2) and (3^2). Step 3: (2\times9=18), so the HCF is (18).
View question detailsStep 1: (72=2^3\times3^2) and (90=2\times3^2\times5). Step 2: The highest powers are (2^3), (3^2), and (5). Step 3: (8\times9\times5=360), so the LCM is (360).
View question detailsStep 1: (12=2^2\times3), (18=2\times3^2), and (30=2\times3\times5). Step 2: The common prime factors in all three numbers are (2) and (3). Step 3: (2\times3=6), so the HCF is (6).
View question detailsStep 1: (12=2^2\times3), (18=2\times3^2), and (30=2\times3\times5). Step 2: Use the highest powers (2^2), (3^2), and (5). Step 3: (4\times9\times5=180), so the LCM is (180).
View question detailsStep 1: (16=2^4), (24=2^3\times3), and (40=2^3\times5). Step 2: The common prime factor is (2), and the smallest power is (2^3). Step 3: (2^3=8), so the HCF is (8).
View question detailsStep 1: (16=2^4), (24=2^3\times3), and (40=2^3\times5). Step 2: Take the highest powers (2^4), (3), and (5). Step 3: (16\times3\times5=240), so the LCM is (240).
View question detailsStep 1: The common prime factors are (2), (3), and (5). Step 2: Their smaller powers are (2), (3), and (5). Step 3: (2\times3\times5=30), so the HCF is (30).
View question detailsStep 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^2), (3^2), and (5). Step 3: (4\times9\times5=180), so the LCM is (180).
View question detailsStep 1: The common prime factors are (2) and (3). Step 2: The smaller powers are (2^2) and (3). Step 3: (2^2\times3=12), so the HCF is (12).
View question detailsQUIZ COMPLETE
