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L.C.M. and H.C.F.

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A prime factorisation of a natural number can be expressed in the exponential form. For example: (i) 48 = 2×2×2×2×3 = 24×3 (ii) 420 = 2×2×3×5×7 = 2² ×3×5×7. Least Common Multiple (abbreviated L.C.M.) of two natural numbers is the smallest natural number which is a multiple of both the numbers. Highest Common Factor (abbreviated H.C.F.) of two natural numbers is the largest common factor (or divisor) of the given natural numbers. In other words, H.C.F. is the greatest element of the set of common factors of the given numbers. H.C.F. is also called Greatest Common Divisor (abbreviated G.C.D.)

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A prime factorisation of a natural number can be expressed in the exponential form. For example: (i) 48 = 2×2×2×2×3 = 24×3 (ii) 420 = 2×2×3×5×7 = 2² ×3×5×7. Least Common Multiple (abbreviated L.C.M.) of two natural numbers is the smallest natural number which is a multiple of both the numbers. Highest Common Factor (abbreviated H.C.F.) of two natural numbers is the largest common factor (or divisor) of the given natural numbers. In other words, H.C.F. is the greatest element of the set of common factors of the given numbers. H.C.F. is also called Greatest Common Divisor (abbreviated G.C.D.) Co-prime numbers: Two natural numbers are called co-prime numbers if they have no common factor other than 1. In other words, two natural numbers are co-prime if their H.C.F. is 1. Some examples of co-prime numbers are: 4, 9; 8, 21; 27, 50. The product of L.C.M. and H.C.F. of two natural numbers = the product of the numbers. Note. In particular, if two natural numbers are co-prime then their L.C.M. = the product of the numbers.