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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 two numbers are (2^3\times3) and (2^2\times3^2), what will be their LCM?EasyLevel 10The HCF of two numbers is (9) and their LCM is (180). What is the product of the two numbers?EasyLevel 10The HCF of two numbers is (12) and their LCM is (144). What is their product?EasyLevel 10If the two numbers are (24) and (36), what is the product of their HCF and LCM?EasyLevel 10If the product of two numbers is (720) and their HCF is (12), what will be their LCM?EasyLevel 10If the product of two numbers is (540) and their LCM is (90), what will be their HCF?EasyLevel 10What is the HCF of (14) and (25)?EasyLevel 10What is the LCM of (14) and (25)?EasyLevel 10What will be the LCM of the co-prime numbers (8) and (15)?EasyLevel 10What will be the HCF of (21) and (35)?EasyLevel 10What will be the LCM of (21) and (35)?EasyLevel 10A shopkeeper has (24) pencils and (36) erasers. He wants to make equal packets. What is the maximum number of packets possible?EasyLevel 10In how many maximum equal boxes can (30), (45), and (60) toffees be divided?EasyLevel 10Two bells ring after every (12) minutes and (18) minutes respectively. After how many minutes will they ring together again?EasyLevel 10Three lights flash at intervals of (10), (15), and (20) seconds. After how many seconds will they flash together again?EasyLevel 10Two ropes of (48) cm and (72) cm are to be cut into equal pieces of maximum length. What will be the length of each piece?EasyLevel 10Two strips of (20) m and (28) m are to be cut into equal pieces of maximum length. What will be the length of each piece?EasyLevel 10Which value is the HCF of (54) and (81)?EasyLevel 10Which value is the LCM of (54) and (81)?EasyLevel 10What is the HCF of (63) and (84)?EasyLevel 10