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We study the hadronic decays of Λ+c to the final states Σ+η and Σ+η′, using an e+e− annihilation data sample of 567 pb−1 taken at a center-of-mass energy of 4.6 GeV with the BESIII detector at the BEPCII collider. We find evidence for the decays Λ+c→Σ+η and Σ+η′ with statistical significance of 2.5σ and 3.2σ, respectively. Normalizing to the reference decays Λ+c→Σ+π0 and Σ+ω, we obtain the ratios of the branching fractions B(Λ+c→Σ+η)B(Λ+c→Σ+π0) and B(Λ+c→Σ+η′)B(Λ+c→Σ+ω) to be 0.35±0.16±0.03 and 0.86±0.34±0.07, respectively. The upper limits at the 90\% confidence level are set to be B(Λ+c→Σ+η)B(Λ+c→Σ+π0)<0.58 and B(Λ+c→Σ+η′)B(Λ+c→Σ+ω)<1.2. Using BESIII measurements of the branching fractions of the reference decays, we determine B(Λ+c→Σ+η)=(0.41±0.19±0.05)% (<0.68%) and B(Λ+c→Σ+η′)=(1.34±0.53±0.21)% (<1.9%). Here, the first uncertainties are statistical and the second systematic. The obtained branching fraction of Λ+c→Σ+η is consistent with the previous measurement, and the branching fraction of Λ+c→Σ+η′ is measured for the first time.