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 will be the LCM of (26) and (39)?EasyLevel 11A class has (32) boys and (48) girls. What can be the maximum number of equal groups?EasyLevel 11A shopkeeper wants to pack (42) apples and (56) oranges in equal bags. What is the maximum number of bags possible?EasyLevel 11Two bells ring at intervals of (15) minutes and (20) minutes. After how many minutes will they ring together again?EasyLevel 11Three indicators glow at intervals of (8), (12), and (16) seconds. After how many seconds will they glow together again?EasyLevel 11Ropes of (60) m and (84) m are to be cut into equal pieces of maximum length. What will be the length of each piece?EasyLevel 11Strips of (54) m and (90) m are to be cut into equal pieces of maximum length. What will be the length of each piece?EasyLevel 11What is the HCF of (75) and (100)?EasyLevel 11What is the LCM of (75) and (100)?EasyLevel 11What is the HCF of (98) and (147)?EasyLevel 11What is the LCM of (98) and (147)?EasyLevel 11If (108=2^2\times3^3) and (180=2^2\times3^2\times5), what is their HCF?EasyLevel 11If (108=2^2\times3^3) and (180=2^2\times3^2\times5), what is their LCM?EasyLevel 11What is the HCF of (27), (54), and (81)?EasyLevel 11What is the LCM of (27), (54), and (81)?EasyLevel 11What is the HCF of (72) and (120)?EasyLevel 11What is the LCM of (72) and (120)?EasyLevel 11The prime factorisation of a number is (2^3\times3^2\times5). What is the number?EasyLevel 11The prime factorisation of a number is (2^4\times3\times5^2). What is the number?EasyLevel 11While finding LCM by prime factorisation, which power is taken?EasyLevel 11