Mathematics
HCF and LCM using prime factorisation
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.
Practice questions
If (x=2^a\times3^6\times5) and (y=2^8\times3^b\times7) have HCF (2^6\times3^4), which values are possible?ExpertLevel 12If (m=2^5\times3^a\times5^2) and (n=2^3\times3^4\times5^b\times11) have LCM (2^5\times3^7\times5^3\times11), which values are correct?ExpertLevel 12A school has (312) answer sheets and (468) question papers. They are to be kept in the maximum number of identical packets so that each packet has the same number of both separately. How many packets can be made?ExpertLevel 12Four devices give signals at intervals of (28), (36), (63), and (84) seconds respectively. They signal together now. After how many seconds will they signal together again?ExpertLevel 12If the HCF of two numbers is (2^5\times3^2) and their LCM is (2^9\times3^4\times5), what will be the total power of (3) in their product?ExpertLevel 12If the HCF of (330) and (462) is (66), what is the ratio of their LCM to their HCF?ExpertLevel 12If (192), (288), and (480) are to be divided into the maximum number of equal parts, what will be the number of parts?ExpertLevel 12What is the smallest number exactly divisible by (121), (144), and (250)?ExpertLevel 12If (p=2^4\times3^2\times5\times7) and (q=2^4\times3^2\times5\times7\times19), which statement about (p) and (q) is correct?ExpertLevel 12The HCF of two numbers is (84) and their LCM is (5460). If the numbers are taken as (84r) and (84s), what is the value of (rs)?ExpertLevel 12If the HCF of (216), (324), and (540) is found, what will be the power of (3) in it?ExpertLevel 12If the LCM of (196), (225), and (308) is found, how many distinct prime factors will it have?ExpertLevel 12If (L) is the LCM and (H) is the HCF of (2^6\times3^2\times5^4) and (2^3\times3^5\times5), what will be the powers of (5) in (L) and (H) respectively?ExpertLevel 12If the HCF of (221), (323), and (437) is found, what is the correct value?ExpertLevel 12If the HCF of (264) and (396) is (132), what is the difference between their LCM and HCF?ExpertLevel 12If a number is divisible by both (2^6\times3^2\times7) and (2^4\times3^5\times13), what will be the power of (3) in the smallest such number?ExpertLevel 12If two numbers are coprime and their product is (1517), what will be their LCM?ExpertLevel 12The prime factorisations of three numbers are (2^5\times3^2\times5), (2^3\times3^4\times7), and (2^4\times3\times11). What will be their HCF?ExpertLevel 12If the LCM of (128), (192), and (343) is found, what will be the power of (7) in it?ExpertLevel 12The HCF of two numbers is (18) and their LCM is (6930). How many unordered pairs of such numbers are possible?ExpertLevel 12