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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, take the highest powers. Step 2: Here the highest powers are (2^3) and (3^2). Step 3: (2^3\times3^2=72), so the LCM is (72).
View question detailsStep 1: For two numbers, product equals HCF multiplied by LCM. Step 2: (9\times180=1620). Step 3: In such questions, first apply this relation and then multiply carefully.
View question detailsStep 1: Product of two numbers (=) HCF (\times) LCM. Step 2: (12\times144=1728). Step 3: While multiplying, avoid missing any digit.
View question detailsStep 1: For two numbers, HCF (\times) LCM equals the product of the numbers. Step 2: (24\times36=864). Step 3: In such questions, you need not always find HCF and LCM separately.
View question detailsStep 1: Use the relation product (=) HCF (\times) LCM. Step 2: LCM (=\frac{720}{12}=60). Step 3: You can check the answer by multiplying (12) and (60).
View question detailsStep 1: For two numbers, product (=) HCF (\times) LCM. Step 2: HCF (=\frac{540}{90}=6). Step 3: In relation-based questions, place the given values carefully.
View question detailsStep 1: (14=2\times7) and (25=5^2). Step 2: They have no common prime factor. Step 3: Therefore, the HCF is (1), and such numbers are co-prime.
View question detailsStep 1: (14=2\times7) and (25=5^2). Step 2: Since they have no common prime factor, include all factors for LCM. Step 3: (2\times7\times25=350), so the LCM is (350).
View question detailsStep 1: (8=2^3) and (15=3\times5). Step 2: They have no common prime factor. Step 3: The LCM of co-prime numbers is their product, so (8\times15=120).
View question detailsStep 1: (21=3\times7) and (35=5\times7). Step 2: The common prime factor is (7). Step 3: Therefore, the HCF is (7).
View question detailsStep 1: (21=3\times7) and (35=5\times7). Step 2: For LCM, take (3), (5), and (7). Step 3: (3\times5\times7=105), so the LCM is (105).
View question detailsStep 1: For the maximum number of equal packets, find the HCF. Step 2: (24=2^3\times3) and (36=2^2\times3^2), so HCF (=2^2\times3=12). Step 3: When maximum equal groups are asked, use HCF.
View question detailsStep 1: For maximum equal boxes, find the HCF of (30), (45), and (60). Step 2: (30=2\times3\times5), (45=3^2\times5), (60=2^2\times3\times5). Step 3: The common part is (3\times5=15), so (15) boxes can be made.
View question detailsStep 1: The time when both bells ring together is the LCM of the two times. Step 2: (12=2^2\times3) and (18=2\times3^2), so LCM (=2^2\times3^2=36). Step 3: For repeated time events, use LCM.
View question detailsStep 1: The next common flashing time is the LCM of (10), (15), and (20). Step 2: (10=2\times5), (15=3\times5), (20=2^2\times5). Step 3: (2^2\times3\times5=60), so the answer is (60) seconds.
View question detailsStep 1: For equal pieces of maximum length, find the HCF. Step 2: (48=2^4\times3) and (72=2^3\times3^2), so HCF (=2^3\times3=24). Step 3: For cutting or dividing into maximum equal parts, use HCF.
View question detailsStep 1: For maximum equal length, find the HCF of (20) and (28). Step 2: (20=2^2\times5) and (28=2^2\times7). Step 3: The common part is (2^2=4), so each piece will be (4) m long.
View question detailsStep 1: (54=2\times3^3) and (81=3^4). 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: (54=2\times3^3) and (81=3^4). Step 2: Take the highest powers (2) and (3^4). Step 3: (2\times81=162), so the LCM is (162).
View question detailsStep 1: (63=3^2\times7) and (84=2^2\times3\times7). Step 2: The common factors are (3) and (7). Step 3: (3\times7=21), so the HCF is (21).
View question detailsQUIZ COMPLETE
