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
What is the greatest number that leaves the same remainder when dividing (489), (654), and (909)?ExpertLevel 10If (x=2^a\times3^5\times5) and (y=2^6\times3^b\times7) have HCF (2^4\times3^3), which values are possible?ExpertLevel 10If (m=2^3\times3^a\times5^2) and (n=2^5\times3^2\times5^b\times11) have LCM (2^5\times3^6\times5^4\times11), which values are correct?ExpertLevel 10In a gathering, there are (198) students and (330) guests. The maximum number of identical groups is to be formed so that each group has the same number of students and guests separately. How many groups can be formed?ExpertLevel 10Three bells ring at intervals of (45), (60), and (84) seconds respectively. If they ring together now, after how many seconds will they ring together again?ExpertLevel 10If the HCF of two numbers is (2^3\times3^2) and their LCM is (2^6\times3^5\times5), what will be the total power of (3) in their product?ExpertLevel 10If the HCF of (154) and (231) is (77), what will be the ratio of their LCM to their HCF?ExpertLevel 10If (96), (160), and (224) are to be divided into the maximum number of equal parts, what will be the number of parts?ExpertLevel 10What is the smallest number exactly divisible by (64), (72), and (125)?ExpertLevel 10If (A=2^4\times3^2\times5) and (B=2^4\times3^2\times5\times11), which statement about (A) and (B) is correct?ExpertLevel 10If the HCF of two numbers is (40) and their LCM is (1680), and the numbers are taken as (40r) and (40s), what is the value of (rs)?ExpertLevel 10If the HCF of (135), (180), and (225) is found, what will be the power of (3) in it?ExpertLevel 10If the LCM of (80), (144), and (225) is found, how many distinct prime factors will it have?ExpertLevel 10If (L) is the LCM and (H) is the HCF of (2^7\times3^2\times5) and (2^4\times3^5\times5^3), what will be the powers of (5) in (L) and (H) respectively?ExpertLevel 10If (H) is the HCF of (121), (143), and (169), what is the value of (H)?ExpertLevel 10If the HCF of two numbers is (32) and their LCM is (1536), what will be the total power of (2) in their product?ExpertLevel 10If the HCF of (180) and (252) is (36), what is the difference between their LCM and HCF?ExpertLevel 10If two numbers are coprime and their product is (899), what will be their LCM?ExpertLevel 10If the HCF of (2^3\times3^2\times5), (2^4\times3\times5^3), and (2^2\times3^4\times7) is found, what will it be?ExpertLevel 10The HCF of two numbers is (15) and their LCM is (420). How many unordered pairs are possible?ExpertLevel 10