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 the HCF of two numbers is (18) and their LCM is (990), and the numbers are (18r) and (18s), what is the value of (rs)?HardLevel 13Which statement is correct for (132) and (308)?HardLevel 13If (A=2^6\times3\times5^2) and (B=2^4\times3^3\times5), what will be the power of (2) in their LCM?HardLevel 13If the LCM of (66), (88), and (121) is found, how many distinct prime factors will it have?HardLevel 13If the HCF of two numbers is (45) and their LCM is (1260), what is correct about their existence?HardLevel 13If two strips of lengths (80) metres and (128) metres are to be cut into equal pieces of maximum length, what will be the length of each piece?HardLevel 13What is the smallest number exactly divisible by (36), (100), and (150)?HardLevel 13Which is the smallest number exactly divisible by (36), (100), and (150)?HardLevel 13If (H=2^2\times3\times5) and (L=2^6\times3^3\times5^2\times7) are respectively the HCF and LCM of two numbers, what is (\frac{L}{H})?HardLevel 13If the HCF of (286) and (429) is (143), what will be their LCM?HardLevel 13If (p=2^3\times5^2) and (q=2^3\times5^2\times7), which statement about (p) and (q) is correct?HardLevel 13If (96), (144), and (192) are to be divided into the maximum number of equal parts, what will be the number of parts?HardLevel 13If the HCF of (2^4\times3^3\times5), (2^2\times3^5\times5^2), and (2^6\times3^2\times7) is found, what will it be?HardLevel 13If the LCM of (44), (77), and (121) is found, what will be the power of (11) in it?HardLevel 13If two numbers are (30u) and (30v), where (u) and (v) are coprime and (uv=26), what will be their LCM?HardLevel 13If the HCF of (216) and (360) is (72), what is the value of (\frac{\text{LCM}}{\text{HCF}})?HardLevel 13Which number will surely be a multiple of both (2^6\times3\times5) and (2^4\times3^3\times7)?HardLevel 13If (a=2^5\times3\times7^2) and (b=2^3\times3^2\times5\times7), which prime factors will appear in their HCF?HardLevel 13If (L) is the LCM and (H) is the HCF of (2^7\times3^2\times5) and (2^5\times3^4\times5^3), what will be the powers of (5) in (L) and (H) respectively?HardLevel 13If the LCM of two numbers is (2^6\times3^3\times11) and their HCF is (2^3\times3), what will be the power of (11) in their product?HardLevel 13