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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

What is the LCM of (49) and (70)?EasyLevel 11What is the HCF of (64) and (80)?EasyLevel 11What is the LCM of (64) and (80)?EasyLevel 11What is the HCF of (15), (25), and (35)?EasyLevel 11What is the LCM of (15), (25), and (35)?EasyLevel 11What will be the HCF of (18), (27), and (45)?EasyLevel 11What will be the LCM of (18), (27), and (45)?EasyLevel 11If (m=2^3\times3\times5) and (n=2^2\times3^2), what is the HCF of (m) and (n)?EasyLevel 11If (m=2^3\times3\times5) and (n=2^2\times3^2), what is the LCM of (m) and (n)?EasyLevel 11If two numbers are (2^4\times3) and (2^2\times3\times7), what will be their HCF?EasyLevel 11If two numbers are (2^4\times3) and (2^2\times3\times7), what will be their LCM?EasyLevel 11The HCF of two numbers is (8) and their LCM is (96). What will be the product of the two numbers?EasyLevel 11The HCF of two numbers is (15) and their LCM is (210). What is their product?EasyLevel 11If the product of two numbers is (1296) and their HCF is (18), what will be their LCM?EasyLevel 11If the product of two numbers is (1680) and their LCM is (280), what will be their HCF?EasyLevel 11If (32) and (72) are two numbers, what is the product of their HCF and LCM?EasyLevel 11What is the HCF of (16) and (27)?EasyLevel 11What is the LCM of (16) and (27)?EasyLevel 11The two co-prime numbers are (9) and (20). What will be their LCM?EasyLevel 11What will be the HCF of (26) and (39)?EasyLevel 11