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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 LCM, choose the highest powers. Step 2: Here the highest powers are (2^5) and (3^2). Step 3: (32\times9=288), so the LCM is (288).
View question detailsStep 1: For two numbers, product (=) HCF (\times) LCM. Step 2: (7\times154=1078). Step 3: In such questions, knowing the two numbers separately is not necessary.
View question detailsStep 1: The product of two numbers equals the product of their HCF and LCM. Step 2: (16\times240=3840). Step 3: Writing the relation first reduces calculation mistakes.
View question detailsStep 1: Use the relation product (=) HCF (\times) LCM. Step 2: LCM (=\frac{2016}{24}=84). Step 3: While dividing, simplify the division carefully.
View question detailsStep 1: For two numbers, product (=) HCF (\times) LCM. Step 2: HCF (=\frac{2700}{300}=9). Step 3: You can check the answer using (9\times300=2700).
View question detailsStep 1: For two numbers, HCF (\times) LCM equals the product of the two numbers. Step 2: (54\times96=5184). Step 3: This shortcut saves time in exams.
View question detailsStep 1: (25=5^2) and (36=2^2\times3^2). Step 2: They have no common prime factor. Step 3: Therefore, the HCF is (1).
View question detailsStep 1: (25=5^2) and (36=2^2\times3^2). Step 2: There is no common prime factor, so the LCM is their product. Step 3: (25\times36=900), so the answer is (900).
View question detailsStep 1: (11) is prime and (18=2\times3^2). Step 2: They have no common prime factor. Step 3: The LCM of co-prime numbers is their product, so (11\times18=198).
View question detailsStep 1: (34=2\times17) and (51=3\times17). Step 2: The common prime factor is (17). Step 3: Therefore, the HCF is (17).
View question detailsStep 1: (34=2\times17) and (51=3\times17). Step 2: For LCM, take (2), (3), and (17). Step 3: (2\times3\times17=102), so the answer is (102).
View question detailsStep 1: For maximum equal groups, find the HCF. Step 2: (36=2^2\times3^2) and (60=2^2\times3\times5), so HCF (=2^2\times3=12). Step 3: When maximum equal distribution is asked, use HCF.
View question detailsStep 1: For the maximum number of equal piles, find the HCF of (48) and (72). Step 2: (48=2^4\times3) and (72=2^3\times3^2), so HCF (=2^3\times3=24). Step 3: Maximum equal piles are found using HCF.
View question detailsStep 1: The next common ringing time is the LCM of the two intervals. Step 2: (18=2\times3^2) and (24=2^3\times3), so LCM (=2^3\times3^2=72). Step 3: For repeated time questions, use LCM.
View question detailsStep 1: The common sound time is the LCM of (6), (9), and (15). Step 2: (6=2\times3), (9=3^2), and (15=3\times5). Step 3: (2\times3^2\times5=90), so the answer is (90) minutes.
View question detailsStep 1: For equal pieces of maximum length, find the HCF. Step 2: (72=2^3\times3^2) and (96=2^5\times3), so HCF (=2^3\times3=24). Step 3: In cutting questions, maximum equal length is found by HCF.
View question detailsStep 1: For maximum equal length, find the HCF of (66) and (110). Step 2: (66=2\times3\times11) and (110=2\times5\times11). Step 3: The common part is (2\times11=22), so each piece will be (22) m long.
View question detailsStep 1: (125=5^3) and (150=2\times3\times5^2). Step 2: The common prime factor is (5), and the smaller power is (5^2). Step 3: (5^2=25), so the HCF is (25).
View question detailsStep 1: (125=5^3) and (150=2\times3\times5^2). Step 2: The highest powers are (2), (3), and (5^3). Step 3: (2\times3\times125=750), so the LCM is (750).
View question detailsStep 1: (121=11^2) and (143=11\times13). Step 2: The common prime factor is (11). Step 3: Therefore, the HCF is (11).
View question detailsQUIZ COMPLETE
