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 (121) and (143)?EasyLevel 12If (144=2^4\times3^2) and (216=2^3\times3^3), what is their HCF?EasyLevel 12If (144=2^4\times3^2) and (216=2^3\times3^3), what is their LCM?EasyLevel 12What is the HCF of (32), (48), and (64)?EasyLevel 12What is the LCM of (32), (48), and (64)?EasyLevel 12What is the HCF of (96) and (144)?EasyLevel 12What is the LCM of (96) and (144)?EasyLevel 12The prime factorisation of a number is (2^2\times3\times11). What is the number?EasyLevel 12The prime factorisation of a number is (2^3\times7^2). What is the number?EasyLevel 12If one number is a multiple of the other, what is the LCM of the two numbers?EasyLevel 12If one number is a multiple of the other, what is the HCF of the two numbers?EasyLevel 12If the HCF of (2160) and (3780) is found using prime factorisation, what is the correct value?HardLevel 10If (840=2^3\times 3\times 5\times 7) and (1260=2^2\times 3^2\times 5\times 7), what is their LCM?HardLevel 10The product of two numbers is (15120) and their HCF is (36). If one number is (216), what is the other number?HardLevel 10The product of two numbers is (15120), and one of the numbers is (216). What is the other number?HardLevel 10The HCF of two numbers is (18) and their LCM is (540). If one number is (90), what is the other number?HardLevel 10If two numbers are (2^3\times 3^2\times 5) and (2^2\times 3^4\times 7), what is the product of their HCF and LCM?HardLevel 10What is the HCF of the three numbers (2^4\times 3^2\times 5), (2^3\times 3^3\times 7), and (2^5\times 3\times 5\times 7)?HardLevel 10What will be the LCM of the three numbers (2^4\times 3^2), (2^2\times 3^5\times 5), and (2^3\times 5^2)?HardLevel 10If the HCF of two numbers is (2^2\times 3) and their LCM is (2^5\times 3^3\times 5), what is the exponent of (2) in the product of the two numbers?HardLevel 10